相关论文: Local limit theory and large deviations for superc…

Under minimal condition, we prove the local convergence of a critical multi-type Galton-Watson tree conditioned on having a large total progeny by types towards a multi-type Kesten's tree. We obtain the result by generalizing Neveu's strong…

In this paper we study the genealogical structure of a Galton-Watson process with neutral mutations, where the initial population is large and mutation rate is small \cite{B2}. Namely, we extend in two directions the results obtained in…

In this paper we show that the random degree constrained process (a time-evolving random graph model with degree constraints) has a local weak limit, provided that the underlying host graphs are high degree almost regular. We, moreover,…

In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem generalizes and…

The motivation for the development of a local finite density theory is discussed. One of the problems related to an instability in the baryon number fluctuation of the chiral symmetry breaking phase of the quark system in the local theory…

In the first part of this paper we give easy and intuitive proofs for the small value probabilities of the martingale limit of a supercritical Galton-Watson process in both the Schr\"oder and the B\"ottcher case. These results are…

We consider a random walk $(Y_N)_{N\geq 0}$ on $\mathbb{R}^2$ generated by successively applying independent random isometries, drawn from a fixed measure $\mu$, to the point $0$. When the support of $\mu$ is finite and includes an…

Consider a random walk in random environment on a supercritical Galton--Watson tree, and let $\tau_n$ be the hitting time of generation $n$. The paper presents a large deviation principle for $\tau_n/n$, both in quenched and annealed cases.…

The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…

We investigate subcritical Galton-Watson branching processes with immigration in a random environment. Using Goldie's implicit renewal theory we show that under general Cram\'er condition the stationary distribution has a power law tail. We…

Given a supercritical branching random walk $\{Z_n\}_{n\geq 0}$ on $\mathbb{R}$, let $Z_n([y,\infty))$ be the number of particles located in $[y,\infty)\subset\mathbb{R}$ at generation $n$. Let $m$ be the mean of the offspring law of…

We present a new large-deviation approach to investigate the critical properties of the Anderson model on the Bethe lattice close to the localization transition in the thermodynamic limit. Our method allows us to study accurately the…

In this paper, we establish a spatial central limit theorem for a large class of supercritical branching, not necessarily symmetric, Markov processes with spatially dependent branching mechanisms satisfying a second moment condition. This…

Let $P(n,m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set $\left\{1, \ldots, n\right\}$ with $m=m(n)$ edges. We determine the (Benjamini-Schramm) local weak limit of $P(n,m)$ in the sparse regime…

The aim of this paper is to study the fluctuations of a general class of supercritical branching Markov processes with non-local branching mechanisms. We show the existence of three regimes according to the size of the spectral gap…

Let $W_t(\theta)$ be the Biggins martingale of a supercritical branching L\'evy process with non-local branching mechanism, and denote by $W_\infty(\theta)$ its limit. In this paper, we first study moment properties of $W_t(\theta)$ and…

We give a necessary and sufficient condition for the convergence in distribution of a conditioned Galton-Watson tree to Kesten's tree. This yields elementary proofs of Kesten's result as well as other known results on local limit of…

In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of…

Consider the matrix products $G_n: = g_n \ldots g_1$, where $(g_{n})_{n\geq 1}$ is a sequence of independent and identically distributed positive random $d\times d$ matrices. Under the optimal third moment condition, we first establish a…

Subcritical catalytic branching random walk on d-dimensional lattice is studied. New theorems concerning the asymptotic behavior of distributions of local particles numbers are established. To prove the results different approaches are used…