## About

14

Publications

306

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60

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Introduction

I am a research mathematician. I work in probability theory, focusing on probabilistic models that arise in statistical physics, such as random polymers, stochastic growth models, and interacting particle systems. I am also interested in connections with combinatorics, random matrices and representation theory.

Additional affiliations

September 2020 - present

July 2018 - August 2020

Education

October 2014 - July 2018

October 2011 - November 2013

October 2008 - November 2011

## Publications

Publications (14)

We study the combinatorial structure of the irreducible characters of the classical groups GLn(C), SO2n+1(C), Sp2n(C), SO2n(C) and the “non-classical” odd symplectic group Sp2n+1(C), finding new connections to the probabilistic model of Last Passage Percolation (LPP). Perturbing the expressions of these characters as generating functions of Gelfand...

We present new probabilistic and combinatorial identities relating three random processes: the oriented swap process (OSP) on n particles, the corner growth process, and the last passage percolation (LPP) model. We prove one of the probabilistic identities, relating a random vector of LPP times to its dual, using the duality between the Robinson–Sc...

We study a discrete-time Markov dynamics on triangular arrays of matrices of order $d\geq 1$, driven by inverse Wishart random matrices. The components of the right edge evolve as multiplicative random walks on positive definite matrices with one-sided interactions and can be viewed as a $d$-dimensional generalisation of log-gamma polymer partition...

We establish analogues of the geometric Pitman $2M-X$ theorem of Matsumoto and Yor and of the classical Dufresne identity, for a multiplicative random walk on positive definite matrices with Beta type II distributed increments. The Dufresne type identity provides another example of a stochastic matrix recursion, as considered by Chamayou and Letac...

We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We establish its fundamental relation to the geometric Robinson-Schensted-Knuth correspondence and to the geometric Schützenberger involution. We also show a number of properties of the geometric Burge corre...

We present new probabilistic and combinatorial identities relating three random processes: the oriented swap process on $n$ particles, the corner growth process, and the last passage percolation model. We prove one of the probabilistic identities, relating a random vector of last passage percolation times to its dual, using the duality between the...

We present new combinatorial and probabilistic identities relating three random processes: the oriented swap process on $n$ particles, the corner growth process, and the last passage percolation model. We prove one of the probabilistic identities, relating a random vector of last passage percolation times to its dual, using the duality between the...

We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We prove a fundamental link with the geometric Robinson-Schensted-Knuth correspondence and with the geometric Sch\"utzenberger involution. We also show a number of properties of the geometric Burge correspon...

We derive Sasamoto’s Fredholm determinant formula for the Tracy-Widom GOE distribution, as well as the one-point marginal distribution of the Airy2→1 process, originally derived by Borodin-Ferrari-Sasamoto, as scaling limits of point-to-line and point-to-half-line directed last passage percolation with exponentially distributed waiting times. The a...

We introduce two families of symmetric polynomials that interpolate between irreducible characters of ${\rm Sp}_{2n}(\mathbb{C})$ and ${\rm SO}_{2n+1}(\mathbb{C})$ and between irreducible characters of ${\rm SO}_{2n}(\mathbb{C})$ and ${\rm SO}_{2n+1}(\mathbb{C})$. We define them as generating functions of certain kinds of Gelfand-Tsetlin patterns a...

This thesis deals with some $(1+1)$-dimensional lattice path models from the KPZ universality class: the directed random polymer with inverse-gamma weights (known as log-gamma polymer) and its zero temperature degeneration, i.e. the last passage percolation model, with geometric or exponential waiting times. We consider three path geometries: point...

We derive Sasamoto's Fredholm determinant formula for the Tracy-Widom GOE distribution, as well as the one-point marginal distribution of the Airy2→1 process, originally derived by Borodin-Ferrari-Sasamoto, as scaling limits of point-to-line and point-to-half-line last passage percolation with exponentially distributed waiting times. The asymptotic...

We study a one dimensional directed polymer model in an inverse-gamma random environment, known as the log-gamma polymer, in three different geometries: point-to-line, point-to-half line and when the polymer is restricted to a half space with end point lying free on the corresponding half line.Via the use of A.N.Kirillov's geometric Robinson-Schens...

In this paper, we deal with the problem of efficiently assessing the higher order vulnerability of a hardware cryptographic circuit. Our main concern is to provide methods that allow a circuit designer to detect early in the design cycle if the implementation of a Boolean-additive masking countermeasure does not hold up to the required protection o...