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We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…

Probability · Mathematics 2017-12-05 Bojan Basrak , Hrvoje Planinic , Philippe Soulier

We prove convergence of renormalized correlations of primary fields, i. e., spins, disorders, fermions and energy densities, in the scaling limit of the critical Ising model in arbitrary finitely connected domains, with fixed (plus or…

Mathematical Physics · Physics 2022-02-24 Dmitry Chelkak , Clément Hongler , Konstantin Izyurov

Consider a set of $n$ vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for…

Probability · Mathematics 2022-09-07 Remco van der Hofstad , Pim van der Hoorn , Neeladri Maitra

In this paper we provide an upper bound for the conjunction probability of independent Gaussian smooth processes and then we prove that this bound is a good approximation with exponentially smaller error. Our result confirms the heuristic…

Probability · Mathematics 2019-09-17 Viet-Hung Pham

We present some correlated fractional counting processes on a finite time interval. This will be done by considering a slight generalization of the processes in Borges et al. (2012). The main case concerns a class of space-time fractional…

Probability · Mathematics 2014-11-10 Luisa Beghin , Roberto Garra , Claudio Macci

Given a homogenous Poisson point process in the plane, we prove that it is possible to partition the plane into bounded connected cells of equal volume, in a translation-invariant way, with each point of the process contained in exactly one…

Probability · Mathematics 2014-10-13 Alexander E. Holroyd , James B. Martin

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In this paper we consider two such likelihood ratios. The first one is an…

Statistics Theory · Mathematics 2010-04-05 Serguei Dachian

The paper contains an exposition of recent as well as old enough results on determinantal random point fields. We start with some general theorems including the proofs of the necessary and sufficient condition for the existence of the…

Probability · Mathematics 2015-06-26 Alexander Soshnikov

We prove the Central Limit Theorem and superpolynomial mixing for environment viewed for the particle process in quasi periodic Diophantine random environment. The main ingredients are smoothness estimates for the solution of the Poisson…

Dynamical Systems · Mathematics 2024-07-24 Klaudiusz Czudek , Dmitry Dolgopyat

For one-dimensional simple random walk in a general i.i.d. scenery and its limiting process we construct a coupling with explicit rate of approximation extending a recent result for Gaussian sceneries due to Khoshnevisan and Lewis.…

Probability · Mathematics 2016-09-07 Endre Csáki , Wolfgang König , Zhan Shi

We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…

Probability · Mathematics 2007-05-23 Mathew D. Penrose , J. E. Yukich

The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…

Probability · Mathematics 2016-02-09 Yi-Ching Yao , Daniel Wei-Chung Miao , Xenos Chang-Shuo Lin

Fix a subset $S \subset \mathbb{R}^n$ of volume at most $c n$ that satisfies $S \cap (-S) = \emptyset$. We consider two point processes in $S$: the first is the Poisson point process of intensity one, and the second is the restriction of a…

Probability · Mathematics 2026-05-12 Boaz Klartag

We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed…

Probability · Mathematics 2007-05-23 Dominic Schuhmacher

Consider the random set composed of particles initially distributed on Zd, d >= 2, according to a Poisson point process of intensity u > 0 and moving as independent simple symmetric random walks, the trap particles. We are interested in the…

Probability · Mathematics 2025-07-22 Gonzalo Panizo , Carlos Martínez

We study the asymptotic behaviour of additive functionals of random walks in random scenery. We establish bounds for the moments of the local time of the Kesten and Spitzer process.These bounds combined with a previous moment convergence…

Dynamical Systems · Mathematics 2021-01-05 Françoise Pene

We show that any strictly quasi-regular generalized Dirichlet form that satisfies the mild structural condition D3 is associated to a Hunt process, and that the associated Hunt process can be approximated by a sequence of multivariate…

Probability · Mathematics 2015-12-15 Vitali Peil , Gerald Trutnau

We study quantitative recurrence to rare events in Countable Markov Shifts with recurrent potentials, focusing on return-time statistics to natural target sets for every point. In the positive recurrent case, return-time processes…

Dynamical Systems · Mathematics 2025-12-16 Dylan Bansard-Tresse

We consider the convex hull of the perturbed point process comprised of $n$ i.i.d. points, each distributed as the sum of a uniform point on the unit sphere $\S^{d-1}$ and a uniform point in the $d$-dimensional ball centered at the origin…

Probability · Mathematics 2019-12-24 Pierre Calka , J. E. Yukich

Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this…

Probability · Mathematics 2024-04-09 Michel Davydov