Related papers: Moderate deviations for the chemical distance in B…
New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on…
The half-orthant model is a partially oriented model of a random medium involving a parameter $p\in [0,1]$, for which there is a critical value $p_c(d)$ (depending on the dimension $d$) below which every point is reachable from the origin.…
We study the Poisson Boolean model with convex bodies which are rotation-invariant distributed. We assume that the convex bodies have regularly varying diameters with indices $-\alpha_1\geq \dots\geq-\alpha_d$ where $\alpha_k >0$ for all…
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…
We consider a fractional porous medium equation that extends the classical porous medium and fractional heat equations. The flow is studied in the space of periodic probability measures endowed with a non-local transportation distance…
The model of Brownian Percolation has been introduced as an approximation of discrete last-passage percolation models close to the axis. It allowed to compute some explicit limits and prove fluctuation theorems for these, based on the…
We continue our study of the chemical (graph) distance inside large critical percolation clusters in dimension two. We prove new estimates, which involve the three-arm probability, for the point-to-surface and point-to-point distances. We…
We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…
Let $L_n$ be the length of the longest common subsequence of two independent i.i.d. sequences of Bernoulli variables of length $n$. We prove that the order of the standard deviation of $L_n$ is $\sqrt{n}$, provided the parameter of the…
In this paper, we prove a central limit theorem and estabilish a moderate deviation principle for stochastic models of incompressible second fluids. The weak convergence method inreoduced by [4] plays an important role.
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…
We modify the Glauber dynamics of the Curie-Weiss model with dissipation in Dai Pra, Fischer, Regoli[2013] by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for…
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…
We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that…
We extend the upper bounds derived for the horizontal and radial chemical distance for 2d Bernoulli percolation in [DHS21, SR20] to the planar random cluster model with cluster weight $1 \le q \le 4$. Along the way, we provide a complete…
Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the two-parameter Poisson-Dirichlet distribution. A sample of size n is selected from the population. The total number of…
The goal of this note is to announce certain results in orbit equivalence theory, especially concerning the approximation of p.m.p. standard equivalence relations by increasing sequence of sub-relations, with applications to the behavior of…
A watermelon is a set of $p$ Bernoulli paths starting and ending at the same ordinate, that do not intersect. In this paper, we show the convergence in distribution of two sorts of watermelons (with or without wall condition) to processes…
Consider an i.i.d. sample from an unknown density function supported on an unknown manifold embedded in a high dimensional Euclidean space. We tackle the problem of learning a distance between points, able to capture both the geometry of…
The general expression of the angular distance between two point sources as measured by an arbitrary observer is given. The modelling presented here is rigorous, covariant and valid in any space-time. The sources of light may be located at…