Hello !I am a Ph.D student at Ecole Normale Supérieure de Paris working on Statistical Physics and Random Matrices under the supervision of Pierre Le Doussal. Prior to this, I read Part III of the Mathematical Tripos at the University of Cambridge, Corpus Christi College and I obtained an M.Sc. and B.Sc. from Ecole polytechnique.

Latest news !
I will attend the CIRM research school on Coulomb Gas, Integrability and Painlevé Equations in March 2019, here is the event link.
01/11/18 : Our last preprint with Pierre Le Doussal is online on this arXiv link, it is entitled "Linear statistics and pushed Coulomb gas at the edge of \(\beta\)random matrices: four paths to large deviations".
The Airy\(_\beta\) point process, \(a_i \equiv N^{2/3} (\lambda_i2)\), describes the eigenvalues \( \lambda_i \) at the edge of the Gaussian \( \beta \) ensembles of random matrices for large matrix size \(N \to \infty\). We study the probability distribution function (PDF) of linear statistics \({\sf L}= \sum_i t \varphi(t^{2/3} a_i)\) for large parameter \( t \). We show the large deviation forms \(\mathbb{E}_{{\rm Airy},\beta}[\exp({\sf L})] \sim \exp( t^2 \Sigma[\varphi])\) and \( P({\mathsf{L}}) \sim \exp( t^2 G(\mathsf{L}/t^2)) \) for the cumulant generating function and the PDF.
We obtain the exact large deviation function \(\Sigma[\varphi]\) using four apparently different methods :
(i) the electrostatics of a Coulomb gas ;
(ii) a random Schrödinger problem, i.e. the stochastic Airy operator ;
(iii) a cumulant expansion ;
(iv) a nonlocal nonlinear differential Painlevé type equation.
Each method was independently introduced previously to obtain the lower tail of the KardarParisiZhang equation. Here we show their equivalence in a more general framework. Our results are obtained for a class of functions \(\varphi\), the monotonous soft walls, containing the monomials \( \varphi(x)=(u+x)_+^\gamma\)and the exponential \( \varphi(x)=e^{u+x} \) and equivalently describe the response of a Coulomb gas pushed at its edge. The small \( u \) behavior of the excess energy \( \Sigma[\varphi]\) exhibits a change at \(\gamma=3/2\) between a nonperturbative hard wall like regime for \(\gamma<3/2\) (third order freetopushed transition) and a perturbative deformation of the edge for \(\gamma>3/2\) (higher order transition).
Applications are given, among them:
(i) truncated linear statistics such as \(\sum_{i=1}^{N_1} a_i\), leading to a formula for the PDF of the ground state energy of \( N_1 \gg 1 \) noninteracting fermions in a linear plus random potential ;
(ii) \(\sim (\beta2)/r^2\) interacting spinless fermions in a trap at the edge of a Fermi gas ;
(iii) traces of large powers of random matrices.
The Airy\(_\beta\) point process, \(a_i \equiv N^{2/3} (\lambda_i2)\), describes the eigenvalues \( \lambda_i \) at the edge of the Gaussian \( \beta \) ensembles of random matrices for large matrix size \(N \to \infty\). We study the probability distribution function (PDF) of linear statistics \({\sf L}= \sum_i t \varphi(t^{2/3} a_i)\) for large parameter \( t \). We show the large deviation forms \(\mathbb{E}_{{\rm Airy},\beta}[\exp({\sf L})] \sim \exp( t^2 \Sigma[\varphi])\) and \( P({\mathsf{L}}) \sim \exp( t^2 G(\mathsf{L}/t^2)) \) for the cumulant generating function and the PDF.
We obtain the exact large deviation function \(\Sigma[\varphi]\) using four apparently different methods :
(i) the electrostatics of a Coulomb gas ;
(ii) a random Schrödinger problem, i.e. the stochastic Airy operator ;
(iii) a cumulant expansion ;
(iv) a nonlocal nonlinear differential Painlevé type equation.
Each method was independently introduced previously to obtain the lower tail of the KardarParisiZhang equation. Here we show their equivalence in a more general framework. Our results are obtained for a class of functions \(\varphi\), the monotonous soft walls, containing the monomials \( \varphi(x)=(u+x)_+^\gamma\)and the exponential \( \varphi(x)=e^{u+x} \) and equivalently describe the response of a Coulomb gas pushed at its edge. The small \( u \) behavior of the excess energy \( \Sigma[\varphi]\) exhibits a change at \(\gamma=3/2\) between a nonperturbative hard wall like regime for \(\gamma<3/2\) (third order freetopushed transition) and a perturbative deformation of the edge for \(\gamma>3/2\) (higher order transition).
Applications are given, among them:
(i) truncated linear statistics such as \(\sum_{i=1}^{N_1} a_i\), leading to a formula for the PDF of the ground state energy of \( N_1 \gg 1 \) noninteracting fermions in a linear plus random potential ;
(ii) \(\sim (\beta2)/r^2\) interacting spinless fermions in a trap at the edge of a Fermi gas ;
(iii) traces of large powers of random matrices.