Related papers: CLT for Ornstein-Uhlenbeck branching particle syst…
In this paper we consider two related stochastic models. The first one is a branching system consisting of particles moving according to a Markov family in R^d and undergoing subcritical branching with a constant rate of V>0. New particles…
In this work, we obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the "spectrum" of partitions of a large integer n (under the Plancherel measure). More specifically, we show that,…
We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…
We consider the asymptotic behavior of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation processes converges in distribution to a generalized…
We present a new approach, inspired by Stein's method, to prove a central limit theorem (CLT) for linear statistics of $\beta$-ensembles in the one-cut regime. Compared with the previous proofs, our result requires less regularity on the…
The spatial logistic branching process is a population dynamics model in which particles move on a lattice according to independent simple symmetric random walks, each particle splits into a random number of individuals at rate one, and…
We consider the determinantal point processes associated with the spectral projectors of a Schr\"odinger operator on $\mathbb{R}$, with a smooth confining potential. In the semiclassical limit, where the number of particles tends to…
We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded…
An $N$-particle system with stochastic interactions is considered. Interactions are driven by a Brownian noise term and total energy conservation is imposed. The evolution of the system, in velocity space, is a diffusion on a…
Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain…
We establish a central limit theorem for the fluctuations of the linear statistics in the $\beta$-ensemble of dimension $N$ at a temperature proportional to $N$ and with confining smooth potential. In this regime, the particles do not…
We study the large deviations of the power injected by the active force for an Active Ornstein-Uhlenbeck Particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in…
In this paper, we study second order fluctuations for the size of the range of a critical branching random walk (BRW) in $\mathbb Z^d$. We consider the BRW with geometric offspring indexed by the Kesten tree, and show that the size of its…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…
It is well known that central order statistics exhibit a central limit behavior and converge to a Gaussian distribution as the sample size grows. This paper strengthens this known result by establishing an entropic version of the CLT that…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
There has been recently a lot of interest in the analysis of the Stein gradient descent method, a deterministic sampling algorithm. It is based on a particle system moving along the gradient flow of the Kullback-Leibler divergence towards…
It is expected that the statistical fluctuations of local observables in large quantum systems obey the central limit theorem, and approximate a normal distribution as their size grows. Here, we prove a version of the Berry-Esseen theorem…
We find a sufficient condition under which a central limit theorem for a stationary linear process is quenched. We find a stationary linear process szatisfying the Maxwell-Woodroofe condition for which the variances of partial sums are…