Related papers: Entry time statistics to different shrinking sets
We describe an approach that allows us to deduce the limiting return times distribution for arbitrary sets to be compound Poisson distributed. We establish a relation between the limiting return times distribution and the probability of the…
Spatio-temporal modelling is an increasingly popular topic in Statistics. Our paper contributes to this line of research by developing the theory, simulation and inference for a spatio-temporal Ornstein-Uhlenbeck process. We conduct…
The waiting time distribution $w(\tau)$, i.e. the probability for a delay $\tau$ between two subsequent transition (`jumps') of particles, is a statistical tool in (quantum) transport. Using generalized Master equations for systems coupled…
We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…
Hitting rate and escape rate are two examples of recurrence laws for a dynamical system, and a general limit connects them. We show that for both Gibbs-Markov systems or any systems with the $\phi$-mixing measure, for a sequence of nested…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
Given a periodic point $\omega$ in a $\psi$-mixing shift with countable alphabet, the sequence $\{S_{n}\}$ of random variables counting the number of multiple returns to shrinking cylindrical neighborhoods of $\omega$ is considered.…
We apply Tsallis's q-indexed entropy to formulate a non-extensive random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. The joint distribution of the matrix elements is given by folding the…
Many-body states that are invariant under particle relabelling, the permutation symmetric states, occur naturally when the system dynamics is described by symmetric processes or collective spin operators. We derive expressions for the…
In the boundary driven symmetric simple exclusion process consider an open set $\ms O$ of density profiles which does not contain the stationary density profile. We prove that the first time the empirical measure visits the set $\ms O$…
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation…
The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions $p_\tau(t)$ at a given time $t$ obtain by integrating out the past and future. We discuss all-time probability distributions…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime (the first passage time) of a system. The statistical distributions that can be obtained out of the mesoscopic description…
The paper introduces sufficient conditions for input-to-state stability (ISS) of a class of impulsive systems with jump maps that depend on time. Such systems can naturally represent an interconnection of several impulsive systems with…
A popular method for sampling from high-dimensional distributions is the \emph{Gibbs sampler}, which iteratively resamples sites from the conditional distribution of the desired measure given the values of the other coordinates. It is…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…
We investigate the properties of uniform doubly stochastic random matrices, that is non-negative matrices conditioned to have their rows and columns sum to 1. The rescaled marginal distributions are shown to converge to exponential…
Exponential families form the backbone of modern statistics and machine learning, but textbooks seldom derive them from first principles in an accessible way. Although minimal sufficiency and the principle of maximum entropy, originating in…
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles.…