33 citations · 46 across the 15 of their papers we have counts for
18 papers · 1 filter
Differentiability of the Leading Lyapunov Exponent of a linear differential equation with random coefficients Application to the Calculation of the Selection Gradient in Random Environments
Philippe Carmona
The study of evolution in temporally fluctuating environments often relies on the analysis of Lyapunov exponents, which quantify the exponential growth of populations. However, whe…
Non-local random deposition models for earthquakes and energy propagation
Philippe Carmona, François Pétrélis, Nicolas Pétrélis
We investigate a new class of non-local random deposition models, initially introduced by physicists to study the field of mechanical constraints (stress) applied along a line or o…
Some deterministic structured population models which are limit of stochastic individual based models
Philippe Carmona
The aim of this paper is to tackle part of the program set by Diekmann et al. in their seminal paper Diekmann et al. (2001). We quote "It remains to investigate whether, and in wha…
Interacting partially directed self-avoiding walk: a probabilistic perspective
Philippe Carmona, Gia Bao Nguyen, Nicolas Pétrélis +1
We review some recent results obtained in the framework of the 2-dimensional Interacting Self-Avoiding Walk (ISAW). After a brief presentation of the rigorous results that have bee…
Limit theorems for Random Walk excursion conditioned to have a typical area
Philippe Carmona, Nicolas Pétrélis
We derive a functional central limit theorem for the excursion of a random walk conditioned on sweeping a prescribed geometric area. We assume that the increments of the random wal…
A shape theorem for the scaling limit of the IPDSAW at criticality
Philippe Carmona, Nicolas Pétrélis
In this paper we give a complete characterization of the scaling limit of the critical Interacting Partially Directed Self-Avoiding Walk (IPDSAW) introduced in Zwanzig and Lauritze…