Related papers: Large Deviations Properties of Maximum Entropy Mar…
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…
Large deviation principles and related results are given for a class of Markov chains associated to the "leaves" in random recursive trees and preferential attachment random graphs, as well as the "cherries" in Yule trees. In particular,…
Understanding how stimuli and synaptic connectivity in uence the statistics of spike patterns in neural networks is a central question in computational neuroscience. Maximum Entropy approach has been successfully used to characterize the…
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
We prove large deviations principles for spectral measures of perturbed (or spiked) matrix models in the direction of an eigenvector of the perturbation. In each model under study, we provide two approaches, one of which relying on large…
We use statistical estimates of the entropy rate of spike train data in order to make inferences about the underlying structure of the spike train itself. We first examine a number of different parametric and nonparametric estimators (some…
We describe a simple method of umbrella trajectory sampling for Markov chains. The method allows the estimation of large-deviation rate functions, for path-extensive dynamic observables, for an arbitrary number of models within a certain…
We establish the weak large deviations principle for empirical measures of Markov chains on $\mathbb R^d$ under mild assumptions. In particular, no irreducibility is assumed and the initial measure may be arbitrary. The proof is entirely…
In many realistic systems, maximum entropy principle (MEP) analysis provides an effective characterization of the probability distribution of network states. However, to implement the MEP analysis, a sufficiently long-time data recording in…
In this short note we consider semi-Markov processes satisfying the condition of direction-time independence (Markov renewal processes). We derive large deviation principles and fluctuation theorems for the empirical current and the…
Maximum Entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a…
Markov chain Monte Carlo (MCMC) methods are one of the most popular classes of algorithms for sampling from a target probability distribution. A rising trend in recent years consists in analyzing the convergence of MCMC algorithms using…
Let $S_N$ be the sum of vector-valued functions defined on a finite Markov chain. An analogue of the Bernstein--Hoeffding inequality is derived for the probability of large deviations of $S_N$ and relates the probability to the spectral gap…
The large deviations at various levels that are explicit for Markov jump processes satisfying detailed-balance are revisited in terms of the supersymmetric quantum Hamiltonian $H$ that can be obtained from the Markov generator via a…
We establish large deviations properties valid for almost every sample path of a class of stationary mixing processes $(X_1,..., X_n,...)$. These properties are inherited from those of $S_n=\sum_{i=1}^nX_i$ and describe how the local…
We consider a family of continuous time symmetric random walks indexed by $k\in \mathbb{N}$, $\{X_k(t),\,t\geq 0\}$. For each $k\in \mathbb{N}$ the matching random walk take values in the finite set of states…
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.
In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…
We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…