Institut Universitaire de France

Averaging principle for jump processes depending on fast ergodic dynamics

Vincent Kagan, Edouard Strickler, Denis Villemonais

We consider a slow-fast stochastic process where the slow component is a jump process on a measurable index set whose transition rates depend on the position of the fast component.…

Quasi-compactness for dominated kernels with application to quasi-stationary distribution theory

Denis Villemonais

We establish a domination principle for positive operators, which provides an upper bound on the essential spectral radius and yields quasi-compactness criteria on weighted supremu…

Strong Disorder for Stochastic Heat Flow and 2D Directed Polymers

Quentin Berger, Francesco Caravenna, Nicola Turchi

The critical 2D Stochastic Heat Flow (SHF) is a universal measure-valued process that provides a notion of solution to the ill-defined 2D stochastic heat equation. We investigate t…

A random polymer approach to the weak disorder phase of the vertex reinforced jump process

Quentin Berger, Alexandre Legrand, Rémy Poudevigne +1

In this paper, we study the transient phase of the Vertex Reinforced Jump Process (VRJP) in dimension $d \geq 3$ . In Sabot, Zeng (2019), the authors introduce a positive martingale…

Linear and uniform in time bound for the binary branching model with Moran type interactions

A M G Cox, E Horton, D Villemonais

In this note, we recall the definition of the binary branching model with Moran type interactions (BBMMI) introduced in [8]. In this interacting particle system, particles evolve,…

Quasi-stationary distribution for kinetic SDEs with low regularity coefficients

Nicolas Champagnat, Tony Lelièvre, Mouad Ramil +2

We consider kinetic SDEs with low regularity coefficients in the setting recently introduced in [6]. For the solutions to such equations, we first prove a Harnack inequality. Using…

Stability of discrete-time Hawkes process with inhibition: towards a general condition

Manon Costa, Pascal Maillard, Anthony Muraro

In this paper, we study a discrete-time analogue of a Hawkes process, modelled as a Poisson autoregressive process whose parameters depend on the past of the trajectory. The model…

Some properties of the principal Dirichlet eigenfunction in Lipschitz domains, via probabilistic couplings

Quentin Berger, Nicolas Bouchot

We study a discrete and continuous version of the spectral Dirichlet problem in an open bounded connected set $Ω \subset R^{d}$ , in dimension $d \geq 2$ . More precisely, consi…

On joint returns to zero of Bessel processes

Quentin Berger, Loïc Béthencourt, Camille Tardif

In this article, we consider joint returns to zero of $n$ Bessel processes ( $n \geq 2$ ): our main goal is to estimate the probability that they avoid having joint returns to zero fo…

Fock's dimer model on the Aztec diamond

Cédric Boutillier, Béatrice de Tilière

We consider the dimer model on the Aztec diamond with Fock's weights, which is gauge equivalent to the model with any choice of positive weight function. We prove an explicit, comp…

Branching diffusion processes and spectral properties of Feynman-Kac semigroup

Pierre Collet, Sylvie Méléard, Jaime San MARTIN

In this article we study the long time behavior of linear functionals of branching diffusion processesas well as the time reversal of the spinal process by means of spectral proper…

Non-linear conductances of Galton-Watson trees and application to the (near) critical random cluster model

Irene Ayuso Ventura, Quentin Berger

In this article, we study concave recursions on trees, which appear widely in information theory through algorithms such as belief propagation, and in statistical mechanics through…

math.PR2024★ 1 cited

Villain action in lattice gauge theory

Ilya Chevyrev, Christophe Garban

We prove that Villain interaction applied to lattice gauge theory can be obtained as the limit of both Wilson and Manton interactions on a larger graph which we call the {\em carpe…

Semigroup of annuli in Liouville CFT

Guillaume Baverez, Colin Guillarmou, Antti Kupiainen +1

In conformal field theory, the semigroup of annuli with boundary parametrisation plays a special role, in that it generates the whole algebra of local conformal symmetries, the so-…

Time-inhomogeneous N-particle Branching Brownian Motion and the continuous random energy model

Alexandre Legrand, Pascal Maillard

The $N$ -particle branching Brownian motion ( $N$ -BBM) is a branching Markov process which describes the evolution of a population of particles undergoing reproduction and selection.…

The *-Vertex Reinforced Jump Process II: random Schrödinger representation

Christophe Sabot, Pierre Tarrès

In this paper we continue the analysis, initiated in the paper *-VRJP I, of the *-Vertex Reinforced Jump Process (*-VRJP), which is a non reversible generalization of the Vertex Re…

The all-time maximum for branching Brownian motion with absorption conditioned on long-time survival

Pascal Maillard, Jason Schweinsberg

We consider branching Brownian motion in which initially there is one particle at $x$ , particles produce a random number of offspring with mean $m + 1$ at the time of branching event…

A continuous random operator associated with the Vertex Reinforced Jump Process on the circle and the real line

V Rapenne, C Sabot

In this paper, we focus on the scaling-limit of the random potential $β$ associated with the Vertex Reinforced Jump Process (VRJP) on one-dimensional graphs. Moreover, we give a fe…

math.PR2023★ 2 cited

Convex minorant trees associated with Brownian paths and the continuum limit of the minimum spanning tree

Nicolas Broutin, Jean-François Marckert

We give an explicit construction of the scaling limit of the minimum spanning tree of the complete graph. The limit object is described using a recursive construction involving the…

A determinantal point process approach to scaling and local limits of random Young tableaux

Jacopo Borga, Cédric Boutillier, Valentin Féray +1

We obtain scaling and local limit results for large random Young tableaux of fixed shape $λ^{0}$ via the asymptotic analysis of a determinantal point process due to Gorin and Rahman…

(Almost) complete characterization of stability of a discrete-time Hawkes process with inhibition and memory of length two

Manon Costa, Pascal Maillard, Anthony Muraro

We consider a discrete-time version of a Hawkes process defined as a Poisson auto-regressive process whose parameters depend on the past of the trajectory. We allow these parameter…