Related papers: Entry time statistics to different shrinking sets
In this paper we investigate quasi-stationary distributions {\mu}_N of stochastic approximation algorithms with constant step size which can be viewed as random perturbations of a time-continuous dynamical system. Inspired by ecological…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
The probability density is a fundamental quantity for characterizing diffusion processes. However, it is seldom known except in a few renowned cases, including Brownian motion and the Ornstein-Uhlenbeck process and their bridges, geometric…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
We study the mixing time of a random walker who moves inside a dynamical random cluster model on the d-dimensional torus of side-length n. In this model, edges switch at rate \mu between open and closed, following a Glauber dynamics for the…
High-diversity assemblages are very common in nature, and yet the factors allowing for the maintenance of biodiversity remain obscure. The competitive exclusion principle and May's complexity-diversity puzzle both suggest that a community…
Let $(B_{i})$ be a sequence of measurable sets in a probability space $(X,\mathcal{B}, \mu)$ such that $\sum_{n=1}^{\infty} \mu (B_{i}) = \infty$. The classical Borel-Cantelli lemma states that if the sets $B_{i}$ are independent, then $\mu…
It is often of interest to know which systems will approach a periodic trajectory when given a periodic input. Results are available for certain classes of systems, such as contracting systems, showing that they always entrain to periodic…
Let $(X,\p_x)$ be a continuous time Markov chain with finite or countable state space $S$ and let $T$ be its first passage time in a subset $D$ of $S$. It is well known that if $\mu$ is a quasi-stationary distribution relatively to $T$,…
Probing deeper into the existing issues regarding the exit probability (EP) in one dimensional dynamical models, we consider several models where the states are represented by Ising spins and the information flows inwards. At zero…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
Exponential families comprise a broad class of statistical models and parametric families like normal distributions, binomial distributions, gamma distributions or exponential distributions. Thereby the formal representation of its…
We consider the interacting Bessel processes, a family of multiple-particle systems in one dimension where particles evolve as individual Bessel processes and repel each other via a log-potential. We consider two limiting regimes for this…
In this paper, a new mixed Poisson distribution is introduced. This new distribution is obtained by utilizing mixing process, with Poisson distribution as mixed distribution and Transmuted Exponential distribution as mixing distribution.…
Low-dimensional, complex systems are often characterized by logarithmically slow dynamics. We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly…
We study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory, which is based on Beck and Cohen's superstatistics. We obtain an analytic expression for the distribution…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
We construct a family of growing finite bounded degree rooted graphs, $G_n$, in which the mixing time for simple random walk, starting at the root, is order $\log |G_n|$. Yet after a quasi - isometry, the ratio of $|G_n|$ over the mixing…
We consider random transformations $T_\omega^n:=T_{\sigma^{n-1}\omega}\circ\cdots\circ T_{\sigma\omega}\circ T_\omega,$ where each map $T_{\omega}$ acts on a complete metrizable space $M$. The randomness comes from an invertible ergodic…
The exponential family of models is defined in a general setting, not relying on probability theory. Some results of information geometry are shown to remain valid. Exponential families both of classical and of quantum mechanical…