Related papers: A Functional Central Limit Theorem for the Becker-…
We describe limit fluctuations of the height function for the open TASEP on the coexistence line under the stationary measure. It is known that the height function satisfies a law of large numbers as the number of sites $n$ goes to infinity…
Optimal control of interacting particles governed by stochastic evolution equations in Hilbert spaces is an open area of research. Such systems naturally arise in formulations where each particle is modeled by stochastic partial…
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…
We examine the fluctuations of the empirical density measure for the colour version of the symmetric nearest neighbour zero range particle systems in dimension one. We show that the weak limit of these fluctuations is the solution of a…
The goal of the present paper is to establish a framework which allows to rigorously determine the large-scale Gaussian fluctuations for a class of singular SPDEs at and above criticality, and therefore beyond the range of applicability of…
We prove a law of large numbers and a functional central limit theorem for the empirical density of a Marcus-Lushnikov model. The limiting density turns out to be the solution of a Smoluchowski equation, and the fluctuations around this…
Consider the random variable $\mathrm{Tr}( f_1(W)A_1\dots f_k(W)A_k)$ where $W$ is an $N\times N$ Hermitian Wigner matrix, $k\in\mathbb{N}$, and choose (possibly $N$-dependent) regular functions $f_1,\dots, f_k$ as well as bounded…
For a system of mean field interacting diffusion on $\mathbb{T}^d$, the empirical measure $\mu^N$ converges to the solution $\mu$ of the Fokker-Planck equation. Refining this mean field limit as a Central Limit Theorem, the fluctuation…
We investigate the asymptotic behaviour of networks of interacting non-linear Hawkes processes modeling a homogeneous population of neurons in the large population limit. In particular, we prove a functional central limit theorem for the…
We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as…
The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optimal rate of convergence. As a second main result, a…
We consider a system of $N$ neurons, each spiking randomly with rate depending on its membrane potential. When a neuron spikes, its potential is reset to $0$ and all other neurons receive an additional amount $h/N$ of potential, where $ h >…
The propagation of chaos and associated law of large numbers for mean-field interacting age-dependent Hawkes processes (when the number of processes n goes to +$\infty$) being granted by the study performed in (Chevallier, 2015), the aim of…
We introduce what we call the second-order Boltzmann-Gibbs principle, which allows to replace local functionals of a conservative, one-dimensional stochastic process by a possibly nonlinear function of the conserved quantity. This…
We consider a diffusion in a Gaussian random environment that is white in time and study the large-scale behavior of the quenched density with respect to the Lebesgue measure. We show that under diffusive rescaling, the fluctuations of the…
We establish limit theorems for the fluctuations of the rescaled occupation time of a $(d,\alpha,\beta)$-branching particle system. It consists of particles moving according to a symmetric $\alpha$-stable motion in $\mathbb{R}^d$. The…
We prove that in the full $L^2$-regime the partition function of the directed polymer model in dimensions $d\geq 3$, if centered, scaled and averaged with respect to a test function $\varphi \in C_c(\mathbb{R}^d)$, converges in distribution…
We introduce a stochastic generalisation of the classical deterministic Floquet-East model, a discrete circuit with the same kinetic constraint as the East model of glasses. We prove exactly that, in the limit of long time and large size,…
We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter $\Delta\to 1^+$ so as to zoom into the ferroelectric/disordered phase critical point) its height function fluctuations converge…
We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the…