Related papers: Large deviation principle for moment map estimatio…
In this article we establish a large deviation principle for the empirical measures of a simple spatially inhomogeneous random walk on $\overline{\mathbb{Z}}$, the two-point compactification of $\mathbb{Z}$. The classical Donsker--Varadhan…
We consider method-of-quantiles estimators of unknown parameters, namely the analogue of method-of-moments estimators obtained by matching empirical and theoretical quantiles at some probability level lambda in (0,1). The aim is to present…
In \cite{FTD1}, we proved the almost sure convergence of eigenvalues of the SYK model, which can be viewed as a type of \emph{law of large numbers} in probability theory; in \cite{FTD2}, we proved that the linear statistic of eigenvalues…
An introduction to numerical large-deviation sampling is provided. First, direct biasing with a known distribution is explained. As simple example, the Bernoulli experiment is used throughout the text. Next, Markov chain Monte Carlo (MCMC)…
We derive a strong law of large numbers, a central limit theorem, a law of the iterated logarithm and a large deviation theorem for so-called deviation means of independent and identically distributed random variables (for the strong law of…
We consider block codes whose rate converges to the channel capacity with increasing block length at a certain speed and examine the best possible decay of the probability of error. We prove that a moderate deviation principle holds for all…
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…
We study an agent-based model of animals marking their territory and evading adversarial territory in one dimension, with respect to the distribution of the size of the resulting territories. In particular, we use sophisticated sampling…
We prove a large deviation principle and give an expression for the rate function, for the last passage time in a Bernoulli environment. The model is exactly solvable and its invariant version satisfies a Burke-type property. Finally, we…
In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and…
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…
We investigate the Large Deviations properties of bootstrapped empirical measure with exchangeable weights. Our main result shows in great generality how the resulting rate function combines the LD properties of both the sample weights and…
A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…
For statistics of rare events in systems obeying a large-deviation principle, the rate function is a key quantity. When numerically estimating the rate function one is always restricted to finite system sizes. Thus, if the interest is in…
This paper investigates the large deviation problem in the sample path space of the nearest-neighbor random walks on regular trees. We establish the sample path large deviation principle for the law of the distance from a nearest random…
We prove that bridges of subelliptic diffusions on a compact manifold, with distinct ends, satisfy a large deviation principle in a space of Holder continuous functions, with a good rate function, when the travel time tends to 0. This leads…
In this paper we prove a Large Deviation Principle for the sequence of symmetrised empirical measures $\frac{1}{n} \sum_{i=1}^{n} \delta_{(X^n_i,X^n_{\sigma_n(i)})}$ where $\sigma_n$ is a random permutation and $((X_i^n)_{1 \leq i \leq…
We prove a large deviations principle for the largest eigenvalue of Gaussian Kronecker matrices, namely matrices defined as the sum of tensors of independent Gaussian matrices in the regime where the dimension of the Gaussian matrices goes…
We consider the random point processes on a measure space X defined by the Gibbs measures associated to a given sequence of N-particle Hamiltonians H^{(N)}. Inspired by the method of Messer-Spohn for proving concentration properties for the…
The Large Deviations Principle (LDP) is verified for a homogeneous diffusion process with respect to a Brownian motion $B_t$, $$ X^\eps_t=x_0+\int_0^tb(X^\eps_s)ds+ \eps\int_0^t\sigma(X^\eps_s)dB_s, $$ where $b(x)$ and $\sigma(x)$ are are…