Elia Bisi

Elia Bisi
TU Wien | TU Wien · Research Unit Mathematical Stochastics

PhD

About

14
Publications
306
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60
Citations
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
TU Wien
Position
  • Professor (Assistant)
July 2018 - August 2020
University College Dublin
Position
  • Researcher
Education
October 2014 - July 2018
The University of Warwick
Field of study
  • Mathematics
October 2011 - November 2013
October 2008 - November 2011

Publications

Publications (14)
Article
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...
Article
Full-text available
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...
Preprint
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...
Preprint
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...
Article
Full-text available
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...
Preprint
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...
Preprint
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...
Preprint
Full-text available
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...
Conference Paper
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...
Preprint
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...
Preprint
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...
Preprint
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...
Article
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...
Article
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...