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Arxiv list of publication 37 different co-authors,

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__Some figures:__676 citations, 20 publications,Arxiv list of publication 37 different co-authors,

ResearchGate profile h-index=10, i10-index=12

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**this link**to find my PhD thesis.## Publications

**[20]**

**Fishnet four-point integrals: integrable representations and thermodynamic limits**

B. Basso, L. J. Dixon, D. A. Kosower,

__A. Krajenbrink__, D. Zhong

**arXiv**, published online May 21, 2021.

**[19]**

**Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion**

S. Scopa,

__A. Krajenbrink__, P. Calabrese, J. Dubail

**arXiv**, published online May 11, 2021.

**[18]**

**The inverse scattering of the Zakharov-Shabat system solves the weak noise theory of the Kardar-Parisi-Zhang equation**

__A. Krajenbrink__, P. Le Doussal

**arXiv**, published online March 31, 2021.

**[17]**

**Interplay between transport and quantum coherences in free fermonic system**

T. Jin, T. Gautié,

__A. Krajenbrink__, P. Ruggiero, T. Yoshimura

**arXiv**, published online March 24, 2021.

**[16]**

**Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics and spiked random matrices: pinning and localization**

__A. Krajenbrink__, P. Le Doussal, N. O'Connell

**Phys. Rev. E**,

**published online April 13, 2021.**

**arXiv**

**[15]**

**From Painlevé to Zakharov-Shabat and beyond: Fredholm determinants and integro-differential hierarchies**

A. Krajenbrink

**J. Phys. A**, published online December 29, 2020.

**arXiv**

**[14]**

**Half-space stationary Kardar-Parisi-Zhang equation**

G. Barraquand,

__A.__

__Krajenbrink__, P. Le Doussal

**J. Stat. Phys.**, published online August 7, 2020.

**arXiv**

**[13]**

**From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics**

T. Jin,

__A.__

__Krajenbrink__, D. Bernard

**Phys. Rev. Lett.**, published online July 21, 2020.

**arXiv**

**[12]**

**Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions**

J. De Nardis,

__A.__

__Krajenbrink__, P. Le Doussal, T. Thiery

**J. Stat. Mech.**

**,**published online April 16, 2020.

**arXiv**

**[11]**

**Probing the large deviations of the Kardar-Parisi-Zhang equation at short time with an importance sampling of directed polymer in random media**

A. K. Hartmann,

__A.__

__Krajenbrink__, P. Le Doussal

**Phys. Rev. E**,

**published online January 29, 2020**

**. arXiv**

**[10]**

**Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-line**

__A.__

__Krajenbrink__, P. Le Doussal

**SciPost Phys**, published online March 4, 2020.

**arXiv**

**[9]**

**Distribution of Brownian coincidences**

__A.__

__Krajenbrink__, B. Lacroix-A-Chez-Toine, P. Le Doussal

**J. Stat Phys**, published online August 23, 2019.

**arXiv**

**[8]**

**On the qubit routing problem**

A. Cowtan, S. Dilkes, R. Duncan,

__A.__

__Krajenbrink__, W. Simmons, S. Sivarajah

**14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)**, published online May 2019.

**arXiv**

**[7]**

**Linear statistics and pushed Coulomb gas at the edge of \(\beta\)-random matrices: four paths to large deviations**

__A. Krajenbrink__, P. Le Doussal

**Europhysics Letters**, published online February 22, 2019.

**arXiv**

**[6] Systematic time expansion for the Kardar-Parisi-Zhang equation, linear statistics of the GUE at the edge and trapped fermions**

__A. Krajenbrink__, P. Le Doussal, S. Prolhac

**Nuclear Physics B**

**,**

**published online September 26, 2018.**

**arXiv**

**[5] Large fluctuations of the KPZ equation in a half-space**

__A. Krajenbrink__, P. Le Doussal

**SciPost Phys**, published online October 12, 2018.

**arXiv**

**[4]**

**Coulomb-gas electrostatics controls large fluctuations of the Kardar-Parisi-Zhang equation**

I. Corwin, P. Ghosal,

__A.__

__Krajenbrink__, P. Le Doussal and L.C. Tsai

**Phys. Rev. Lett**, published online August 8, 2018.

**arXiv**

**[3] Simple derivation of the \( (-\lambda H)^{5/2}\) tail for the 1D KPZ equation**

__A. Krajenbrink__, P. Le Doussal

**J. Stat. Mech**, published online June 26, 2018.

**arXiv**

****

**[2] Exact short-time height distribution in the one-dimensional Kardar-Parisi-Zhang equation with Brownian initial condition**

__A. Krajenbrink__, P. Le Doussal

**Phys. Rev. E Rapid Communication**, published online August 14, 2017.

**arXiv**

**[1] Atom-by-atom assembly of defect-free one-dimensional cold atom arrays**

M. Endres*, H. Bernien*, A. Keesling*, H. Levine*, E.R. Anschuetz,

__A. Krajenbrink__, C. Senko, V. Vuletic, M. Greiner, M. D. Lukin

*contributed equally

**Science**, published online November 3, 2016.

**arXiv**

Highlighted by

**MIT news**.

During my master degree in Cambridge, I wrote an essay entitled

*"Essay on Tensor Network Renormalization"*under the supervision of Matthew Wingate.__Here is a link to view it__## Talks / Seminars

[8] A journey from classical integrability to the large deviations of the kardar-parisi-zhang equation

In this talk, I will revisit the problem of the large deviations of the Kardar-Parisi-Zhang (KPZ) equation in one dimension at short time by introducing a novel approach which combines field theoretical, probabilistic and integrable techniques. My goal will be to expand the program of the weak noise theory, which maps the large deviations onto a non-linear hydrodynamic problem, and to unveil its complete solvability through a connection to the integrability of the Zakharov-Shabat system. I will show that this approach paves the path to understand the large deviations for general initial geometry.

This is based on the work arXiv:2103.17215 with P. Le Doussal.

This is based on the work arXiv:2103.17215 with P. Le Doussal.

-> Université Catholique de Louvain, June 23, 2021

-> Melbourne - Bielefeld joint seminar on Random Matrices and Applications, June 30, 2021

-> MSRI postdoc seminar "Universality and Integrability in Random Matrix Theory and Interacting Particle Systems", July 19, 2021

-> Melbourne - Bielefeld joint seminar on Random Matrices and Applications, June 30, 2021

-> MSRI postdoc seminar "Universality and Integrability in Random Matrix Theory and Interacting Particle Systems", July 19, 2021

[7] Fredholm determinants, integro-differential Painlevé equations and a Fresh look on the zakharov-shabat system

As Fredholm determinants are more and more frequent in the context of stochastic integrability, I discuss in this talk the existence of a common framework in many integrable systems where they appear. This consists in a hierarchy of equations, akin to the Zakharov-Shabat system, connecting an integro-differential extension of the Painlevé II hierarchy, the finite-time solutions of the Kardar-Parisi-Zhang equation and multi-critical fermions at finite temperature.

**click here to get the slides**

-> Matrix Institute, "Integrability and Combinatorics at Finite Temperature", June 8, 2021

[6] Fredholm determinants, exact solutions to the Kardar-Parisi-Zhang equation and integro-differential Painlevé equations

**click here to get the slides**

-> IPADEGAN network - SISSA "Integrable systems around the world", September 16, 2020

-> University of Michigan - Department of Mathematics "Integrable Systems and Random Matrix Theory", October 26, 2020

-> Institut Henri Poincaré - séminaire MEGA, December 11, 2020

[5] PhD defense. Beyond the typical fluctuations: a journey to the large deviations in the Kardar-Parisi-Zhang growth model

Throughout this Ph.D thesis, we will study the Kardar-Parisi-Zhang (KPZ) stochastic growth model in \(1+1\) dimensions and more particularly the equation which governs it. The goal of this thesis is two-fold. Firstly, it aims to review the state of the art and to provide a detailed picture of the search of exact solutions to the KPZ equation, of their properties in terms of large deviations and also of their applications to random matrix theory or stochastic calculus. Secondly, is it intended to express a certain number of open questions at the interface with integrability theory, random matrix theory and Coulomb gas theory.

This thesis is divided in three distinct parts related to (i) the exact solutions to the KPZ equation, (ii) the short-time solutions expressed by a Large Deviation Principle and the associated rate functions and (iii) the solutions at large time and their extensions to linear statistics at the edge of random matrices.

We will present the new results of this thesis including (a) a new solution to the KPZ equation at all times in a half-space, (b) a general methodology to establish at short time a Large Deviation Principle for the solutions to the KPZ equation from their representation in terms of Fredholm determinant and (c) the unification of four methods allowing to obtain at large time a Large Deviation Principle for the solution to the KPZ equation and more generally to investigate linear statistics at the soft edge of random matrices.

This thesis is divided in three distinct parts related to (i) the exact solutions to the KPZ equation, (ii) the short-time solutions expressed by a Large Deviation Principle and the associated rate functions and (iii) the solutions at large time and their extensions to linear statistics at the edge of random matrices.

We will present the new results of this thesis including (a) a new solution to the KPZ equation at all times in a half-space, (b) a general methodology to establish at short time a Large Deviation Principle for the solutions to the KPZ equation from their representation in terms of Fredholm determinant and (c) the unification of four methods allowing to obtain at large time a Large Deviation Principle for the solution to the KPZ equation and more generally to investigate linear statistics at the soft edge of random matrices.

**click here to get the slides**

-> Ecole Normale Supérieure, June 20, 2019

[4]

**Linear statistics and pushed Coulomb-gas at the soft edge of random matrices : four paths to large deviations**In this talk, I will consider the classical problem of linear statistics in random matrix theory. This amounts to study the distribution of the sum of a certain function of the matrix eigenvalues. Varying this function, this problem can describe fluctuations of conductance, shot noise, Renyi entropy, center of mass of interfaces, particle number…

This problem has been extensively studied for the bulk of the eigenvalues (macroscopic linear statistics) where interesting phase transitions have been unveiled but not so much at the edge of the spectrum (microscopic linear statistics) on which I will focus.

In particular, I will introduce four methods to solve this problem, show their equivalence and I will discuss the physical applications of these results (large deviations of the solution of the Kardar-Parisi-Zhang equation, existence of phase transitions with continuously varying exponent and possible experimental realization of this setup with non-intersecting Brownian interfaces).

This problem has been extensively studied for the bulk of the eigenvalues (macroscopic linear statistics) where interesting phase transitions have been unveiled but not so much at the edge of the spectrum (microscopic linear statistics) on which I will focus.

In particular, I will introduce four methods to solve this problem, show their equivalence and I will discuss the physical applications of these results (large deviations of the solution of the Kardar-Parisi-Zhang equation, existence of phase transitions with continuously varying exponent and possible experimental realization of this setup with non-intersecting Brownian interfaces).

**click here to get the slides**

-> LPTMS, Paris-Sud Orsay, November 27, 2018

-> King's College London, March 20, 2019

-> Université de Lorraine Nancy, June 13, 2019

[3]

**A bottom-up approach to the Kardar-Parisi-Zhang equation for interface growth : recent developments**In this talk, I will review the celebrated Kardar-Parisi-Zhang (KPZ) equation (>3400 citations for the original paper!) and show that it describes a variety of systems through experimental observations (interface growth, chemical reaction fronts…). Starting from scratch, I will discuss the different techniques commonly used in the physics literature to study the KPZ equation (the mapping to the directed polymer, the replica method, the quantum delta Bose gas, the Fredholm determinant and its cumulant expansion) and explain how they allowed to obtain exact solutions in 1+1 dimensions. Finally, I will describe recent developments on the large fluctuations through exact short-time solutions along with recent numerical progress.

This talk is made to be accessible to non-specialists and will tackle at the same time theoretical and computational aspects of the KPZ equation.

This talk is made to be accessible to non-specialists and will tackle at the same time theoretical and computational aspects of the KPZ equation.

**click here to get the slides**

-> University of Oldenburg, April 26, 2018

-> École Normale Supérieure, January 14, 2019

[2]

**Recent short-time developments on the solutions of the KPZ equation**-> University College Dublin, April 17, 2018 (joint seminar with Pierre Le Doussal)

[1]

**Exact short time solutions of the KPZ equation... ...from a physicist's point of view**In the past decade, explicit solutions have been found for the Kardar-Parisi-Zhang (KPZ) equation. Quite remarkably, they always express the moment generating function of the Cole-Hopf solution of the KPZ equation as a Fredholm Pfaffian or Fredholm Determinant. These algebraic structures are quite common in the field of Random Matrix Theory (RMT) and Determinant Point Processes and therefore allow to draw connexions between asymptotic RMT distributions (Tracy-Widom distribution), non-interacting fermions at finite temperature in quantum mechanics and height solutions of the KPZ equation.

I will first review the techniques commonly used in the physics literature to study the KPZ equation (the replica method, the Bethe Ansatz solution of the Lieb-Liniger model) and show how it has allowed to obtain solutions for the KPZ equation. I will then focus on the Brownian initial condition and show how to extract the exact distribution of the solution of the KPZ equation from its Fredholm determinant representation at short time in terms of a Large Deviation Principle.

For this initial condition, it has been found by Janas, Kamenev and Meerson (2016) using Weak Noise Theory that the large deviation function at short time exhibits a second-order phase transition. Starting from the exact Fredholm determinant obtained by Imamura and Sasamoto (2012), I will prove this statement, provide the analytic expression of the critical field where the transition occurs and compare my predictions with the numerical estimates of Janas, Kamenev and Meerson.

I will first review the techniques commonly used in the physics literature to study the KPZ equation (the replica method, the Bethe Ansatz solution of the Lieb-Liniger model) and show how it has allowed to obtain solutions for the KPZ equation. I will then focus on the Brownian initial condition and show how to extract the exact distribution of the solution of the KPZ equation from its Fredholm determinant representation at short time in terms of a Large Deviation Principle.

For this initial condition, it has been found by Janas, Kamenev and Meerson (2016) using Weak Noise Theory that the large deviation function at short time exhibits a second-order phase transition. Starting from the exact Fredholm determinant obtained by Imamura and Sasamoto (2012), I will prove this statement, provide the analytic expression of the critical field where the transition occurs and compare my predictions with the numerical estimates of Janas, Kamenev and Meerson.

**click here to get the slides**

-> University of Warwick, December 7, 2017

## Referee & reviewer activities

*Physics journals:*

- Journal of Statistical Physics
- Physical Review E

*Maths journals:*

- Annales de l'Institut Henri Poincaré
- Communication in Mathematical Physics
- The "Random Matrices" book of the IAS / Park City Mathematics Series

*Universities and committees:*

- National Fund for Scientific and Technological Research (Chile)
- Graduate School of Xi'An Jiaotong-Liverpool University (China)

## Conferences / Schools attended

Clean and disordered systems out of equilibrium,

CIRM research school on Coulomb Gas, Integrability and Painlevé Equations,

The Dynamics of Quantum Information,

Hausdorff School on Log-correlated Fields,

Boulder School 2017 : Frustrated and Disordered systems,

Research Program on Random Matrices, organized by A. Borodin, I. Corwin and A. Guionnet,

Lectures on Statistical Field Theories,

2nd French Russian conference - random geometry and physics,

Quantum Machine Learning,

The Tony and Pat Houghton Conference on non-equilibrium statistical mechanics,

Rencontres d'été de physique de l'infiniment grand à l'infiniment petit,

*Cargese*, September 14-18 2020CIRM research school on Coulomb Gas, Integrability and Painlevé Equations,

*CIRM Luminy*, March 11-15 2019The Dynamics of Quantum Information,

*KITP Santa Barbara*, August 27 - October 19 2018Hausdorff School on Log-correlated Fields,

*Bonn,*June 11-14 2018Boulder School 2017 : Frustrated and Disordered systems,

*Boulder,*July 3-28 2017Research Program on Random Matrices, organized by A. Borodin, I. Corwin and A. Guionnet,

*IAS /**Park City Mathematics Institute,*June 25 - July 15 2017Lectures on Statistical Field Theories,

*Galileo Galilei Institute,*February 6-17 20172nd French Russian conference - random geometry and physics,

*Institut Henri Poincaré*, October 17-21 2016Quantum Machine Learning,

*Perimeter Institute,* August 8-12 2016The Tony and Pat Houghton Conference on non-equilibrium statistical mechanics,

*ICERM*, May 4-5 2015Rencontres d'été de physique de l'infiniment grand à l'infiniment petit,

*Orsay*, July 15-26 2013## Visits

I have had the chance to visit:

- Malte Henkel, Université de Lorraine Nancy (June 2019)

- Yan Fyodorov, King's College London (March 2019)

- Alexander Hartmann, University of Oldenburg (April 2018)

- Neil O'Connell, University of Bristol (April 2017) & University College Dublin (April 2018)

- Sylvain Prolhac, Université Paul Sabatier, Toulouse (Mars 2018)

- Nikos Zygouras, University of Warwick (December 2017)

- Malte Henkel, Université de Lorraine Nancy (June 2019)

- Yan Fyodorov, King's College London (March 2019)

- Alexander Hartmann, University of Oldenburg (April 2018)

- Neil O'Connell, University of Bristol (April 2017) & University College Dublin (April 2018)

- Sylvain Prolhac, Université Paul Sabatier, Toulouse (Mars 2018)

- Nikos Zygouras, University of Warwick (December 2017)