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Consider the inhomogeneous Erd\H{o}s-R\'enyi random graph (ERRG) on $n$ vertices for which each pair $i,j\in\{1,\ldots,n\}$, $i\neq j$ is connected independently by an edge with probability $r_n(\frac{i-1}{n},\frac{j-1}{n})$, where…

Probability · Mathematics 2022-08-23 Maarten Markering

The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.

Probability · Mathematics 2007-05-23 F. Klebaner , R. Liptser

We recover the Donsker-Varadhan large deviations principle (LDP) for the empirical measure of a continuous time Markov chain on a countable (finite or infinite) state space from the joint LDP for the empirical measure and the empirical flow…

Probability · Mathematics 2013-01-01 L. Bertini , A. Faggionato , D. Gabrielli

The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear…

Probability · Mathematics 2019-11-18 A. Logachov , O. Logachova , A. Yambartsev

We prove the large deviation principle for the trajectory of a broad class of mean field interacting Markov jump processes via a general analytic approach based on viscosity solutions. Examples include generalized Ehrenfest models as well…

Probability · Mathematics 2016-06-24 Richard Kraaij

Advances in mobile computing technologies have made it possible to monitor and apply data-driven interventions across complex systems in real time. Markov decision processes (MDPs) are the primary model for sequential decision problems with…

Methodology · Statistics 2018-03-20 Longshaokan Wang , Eric B. Laber , Katie Witkiewitz

The configuration model is a sequence of random graphs constructed such that in the large network limit the degree distribution converges to a pre-specified probability distribution. The component structure of such random graphs can be…

Probability · Mathematics 2019-12-12 Shankar Bhamidi , Amarjit Budhiraja , Paul Dupuis , Ruoyu Wu

We initiate a study of large deviations for block model random graphs in the dense regime. Following Chatterjee-Varadhan(2011), we establish an LDP for dense block models, viewed as random graphons. As an application of our result, we study…

Probability · Mathematics 2025-09-17 Christian Borgs , Jennifer Chayes , Julia Gaudio , Samantha Petti , Subhabrata Sen

We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean-Vlasov equation depending on , the scaling parameter separating the time scale of the slow…

Analysis of PDEs · Mathematics 2021-08-09 Julien Barré , Cedric Bernardin , Raphaël Chétrite , Yash Chopra , Mauro Mariani

We prove a large deviation principle for the point process associated to $k$-element connected components in $\mathbb R^d$ with respect to the connectivity radii $r_n\to\infty$. The random points are generated from a homogeneous Poisson…

Probability · Mathematics 2022-10-19 Christian Hirsch , Takashi Owada

We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps,…

Quantum Physics · Physics 2014-04-03 Bassano Vacchini

We consider a system of stochastic interacting particles in $\mathbb{R}^d$ and we describe large deviations asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviations principle (LDP) is established for the…

Probability · Mathematics 2020-11-17 Carlo Orrieri

We give a criterion to determine the large deviation rate functions for abstract dynamical systems on towers. As an application of this criterion we show the level 2 large deviation principle for some class of smooth interval maps with…

Dynamical Systems · Mathematics 2008-01-17 Yong Moo Chung

We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of…

Probability · Mathematics 2009-11-13 Yuri Bakhtin , Christine Heitsch

We consider a system of $N$ particles whose interactions are characterized by a (weighted) graph $G^N$. Each particle is a node of the graph with an internal state. The state changes according to Markovian dynamics that depend on the states…

Probability · Mathematics 2024-05-15 Sebastian Allmeier , Nicolas Gast

Large deviation theory is a branch of probability theory that is devoted to a study of the "rate" at which empirical estimates of various quantities converge to their true values. The object of study in this paper is the rate at which…

Statistics Theory · Mathematics 2013-09-17 Mathukumalli Vidyasagar

Graph-based change point detection (CPD) play an irreplaceable role in discovering anomalous graphs in the time-varying network. While several techniques have been proposed to detect change points by identifying whether there is a…

Social and Information Networks · Computer Science 2022-12-20 Yongshun Gong , Xue Dong , Jian Zhang , Meng Chen

A trajectorial large deviation principle is established in a mean field thermodynamic limit for a multiclass loss network with diminishing rates, which may have several stable equilibria. The large deviation limit is identified as a unique…

Probability · Mathematics 2022-05-23 Anatolii A. Puhalskii

We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic…

Analysis of PDEs · Mathematics 2014-10-24 Vojkan Jaksic , Vahagn Nersesyan , Claude-Alain Pillet , Armen Shirikyan

This article studies deep neural network expression rates for optimal stopping problems of discrete-time Markov processes on high-dimensional state spaces. A general framework is established in which the value function and continuation…

Probability · Mathematics 2022-10-20 Lukas Gonon