English
Related papers

Related papers: Fully explicit large deviation inequalities for em…

200 papers

We establish a new Bernstein-type deviation inequality for general (non-reversible) discrete-time Markov chains via an elementary approach. More robust than existing works in the literature, our result only requires the Markov chain to…

Probability · Mathematics 2025-10-07 De Huang , Xiangyuan Li

Degrading performance of indexing schemes for exact similarity search in high dimensions has long since been linked to histograms of distributions of distances and other 1-Lipschitz functions getting concentrated. We discuss this…

Data Structures and Algorithms · Computer Science 2012-04-13 Vladimir Pestov

A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…

Probability · Mathematics 2014-10-17 Markus Fischer

We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…

Statistical Mechanics · Physics 2019-10-21 Piergiulio Tempesta , Henrik Jeldtoft Jensen

We formulate the large deviations for a class of two scale chemical kinetic processes motivated from biological applications. The result is successfully applied to treat a genetic switching model with positive feedbacks. The corresponding…

Probability · Mathematics 2016-04-05 Tiejun Li , Feng Lin

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…

Probability · Mathematics 2023-07-17 Zachary Bezemek , Konstantinos Spiliopoulos

An identity between two versions of the Chernoff bound on the probability a certain large deviations event, is established. This identity has an interpretation in statistical physics, namely, an isothermal equilibrium of a composite system…

Information Theory · Computer Science 2007-07-13 Neri Merhav

An analogue of Talagrand's convex distance for binomial and Poisson point processes is defined. A corresponding large deviation inequality is proved.

Probability · Mathematics 2013-06-05 Matthias Reitzner

We consider a non-stationary Cox-Ingersoll-Ross process. We establish a sharp large deviation principle for the maximum likelihood estimator of its drift parameter.

Probability · Mathematics 2018-06-22 marie du Roy de Chaumaray

We prove an energy estimate for the polar empirical measure of the two-dimensional symmetric simple exclusion process. We deduce from this estimate and from results in reference [2] large deviations principles for the polar empirical…

Probability · Mathematics 2017-04-07 Claudio Landim , Chih-Chung Chang , Tzong-Yow Lee

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful…

Neurons and Cognition · Quantitative Biology 2018-08-15 Rodrigo Cofre , Cesar Maldonado , Fernando Rosas

Conformal prediction is a powerful framework for constructing prediction sets with valid coverage guarantees in multi-class classification. However, existing methods often rely on a single score function, which can limit their efficiency…

Machine Learning · Statistics 2025-03-05 Rui Luo , Zhixin Zhou

Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…

Statistics Theory · Mathematics 2024-01-18 Nabarun Deb , Debarghya Mukherjee

This paper is focused on derivations of data-processing and majorization inequalities for $f$-divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first…

Information Theory · Computer Science 2020-01-08 Igal Sason

In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the…

Probability · Mathematics 2020-07-02 Jasper Hoeksema , Thomas Holding , Mario Maurelli , Oliver Tse

This paper deals with rare events in a general {interacting gas} at high temperature, by means of Large Deviations Principles. The main result is an LDP for the tagged empirical field, which features the competition of an energy term and an…

Probability · Mathematics 2025-06-17 David Padilla-Garza

A large deviations principle is established for the joint law of the empirical measure and the flow measure of a renewal Markov process on a finite graph. We do not assume any bound on the arrival times, allowing heavy tailed distributions.…

Probability · Mathematics 2014-02-18 Mauro Mariani , Lorenzo Zambotti

In this paper we establish a large deviations type estimate for strongly mixing Markov chains with respect to the Lp norm. As applications we derive such estimates for the iterates of a locally constant random cocycle with mixed rank, as…

Dynamical Systems · Mathematics 2026-02-10 Anselmo Pontes

The aim of this paper is to improve the large deviation principle for the number of descents in a random permutation by establishing a sharp large deviation principle of any order. We shall also prove a sharp large deviation principle of…

Probability · Mathematics 2024-07-09 Bernard Bercu , Michel Bonnefont , Luis Fredes , Adrien Richou

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