Related papers: Gaussian approximation for rooted edges in a rando…

We consider Gibbs distributions on finite random plane trees with bounded branching. We show that as the order of the tree grows to infinity, the distribution of any finite neighborhood of the root of the tree converges to a limit. We…

Let $f = \sum_{k=0}^n \varepsilon_k z^k$ be a random polynomial, where $\varepsilon_0,\ldots ,\varepsilon_n$ are iid standard Gaussian random variables, and let $\zeta_1,\ldots,\zeta_n$ denote the roots of $f$. We show that the point…

We consider bootstrap percolation and diffusion in sparse random graphs with fixed degrees, constructed by configuration model. Every node has two states: it is either active or inactive. We assume that to each node is assigned a…

We study a model of random $\mathcal{R}$-enriched trees that is based on weights on the $\mathcal{R}$-structures and allows for a unified treatment of a large family of random discrete structures. We establish distributional limits…

We continue the study of the level-set percolation of the discrete Gaussian free field (GFF) on regular trees in the critical regime, initiated in arXiv:2302.02753. First, we derive a sharp asymptotic estimate for the probability that the…

We establish a central limit theorem for (a sequence of) multivariate martingales which dimension potentially grows with the length $n$ of the martingale. A consequence of the results are Gaussian couplings and a multiplier bootstrap for…

We prove an invariance principle for linearly edge reinforced random walks on $\gamma$-stable critical Galton-Watson trees, where $\gamma \in (1,2]$ and where the edge joining $x$ to its parent has rescaled initial weight $d(\rho,…

For the critical level-set of the Gaussian free field on the metric graph of $\mathbb Z^d$, we consider the one-arm probability $\theta_d(N)$, i.e., the probability that the boundary of a box of side length $2N$ is connected to the center.…

In the model of randomly perturbed graphs we consider the union of a deterministic graph $\mathcal{G}_\alpha$ with minimum degree $\alpha n$ and the binomial random graph $\mathbb{G}(n,p)$. This model was introduced by Bohman, Frieze, and…

In this paper, we refine the Berry-Esseen bounds for the multivariate normal approximation of Polyak-Ruppert averaged iterates arising from the linear stochastic approximation (LSA) algorithm with decreasing step size. We consider the…

By the Lindeberg principle, we develop in this paper an approximation to one dimensional (possibly) asymmetric $\alpha$-stable distributions with $\alpha \in (0,2)$ in the smooth Wasserstein distance. It is the first time that the general…

The ellipsoid fitting conjecture of Saunderson, Chandrasekaran, Parrilo and Willsky considers the maximum number $n$ random Gaussian points in $\mathbb{R}^d$, such that with high probability, there exists an origin-symmetric ellipsoid…

An additive functional of a rooted tree is a functional that can be calculated recursively as the sum of the values of the functional over the branches, plus a certain toll function. Janson recently proved a central limit theorem for…

We introduce a dynamic random hypergraph model constructed from a bipartite graph. In this model, both vertex sets of the bipartite graph are generated by marked Poisson point processes. Vertices of both vertex sets are equipped with marks…

There is a long history of establishing central limit theorems for Markov chains. Quantitative bounds for chains with a spectral gap were proved by Mann and refined later. Recently, rates of convergence for the total variation distance were…

We establish novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters (weights and biases) and Lipschitz activation functions, in the wide limit. Our bounds apply for the joint output of a network…

Consider a rooted infinite Galton-Watson tree with mean offspring number $m>1$, and a collection of i.i.d. positive random variables $\xi_e$ indexed by all the edges in the tree. We assign the resistance $m^d \xi_e$ to each edge $e$ at…

We study how eigenvectors of random regular graphs behave when projected onto fixed directions. For a random $d$-regular graph with $N$ vertices, where the degree $d$ grows slowly with $N$, we prove that these projections follow…

We study the asymptotic behavior of the maximum interpoint distance of random points in a $d$-dimensional set with a unique diameter and a smooth boundary at the poles. Instead of investigating only a fixed number of $n$ points as $n$ tends…

We obtain a Central Limit Theorem for the normalized number of real roots of a square Kostlan-Shub-Smale random polynomial system of any size as the degree goes to infinity. A study of the asymptotic variance of the number of roots is…