Related papers: On random topological Markov chains with big image…

Given a set $S=\{x^2+c_1,\dots,x^2+c_s\}$ defined over a field and an infinite sequence $\gamma$ of elements of $S$, one can associate an arboreal representation to $\gamma$, generalizing the case of iterating a single polynomial. We study…

Markov random fields are common prior distributions used in Bayesian inverse imaging problems. In particular, difference priors assign probability distributions to differences between neighbouring pixels, such as Gaussian, Laplace, or…

We present a relative form of the Toponogov comparison theorem.

A theorem on subwavelength imaging with arrays of discrete sources is formulated. This theorem is analogous to the Kotelnikov (also named Nyquist-Shannon) sampling theorem as it represents the field at an arbitrary point of space in terms…

Denote by $\mathcal{H}_k (n,p)$ the random $k$-graph in which each $k$-subset of $\{1... n\}$ is present with probability $p$, independent of other choices. More or less answering a question of Balogh, Bohman and Mubayi, we show: there is a…

Let $a_n$ be the random increasing sequence of natural numbers which takes each value independently with decreasing probability of order $n^{-\alpha}$, $0 < \alpha < 1/2$. We prove that, almost surely, for every measure-preserving system…

We will represent the so-called Perron-Frobenius eigenvector (if exists) for infinite non-negative matrix $A$ and Metzler matrix by using its corresponding Markov chain with probability transition function.

We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…

We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key…

We prove an ergodic theorem for Markov chains indexed by the Ulam-Harris-Neveu tree over large subsets with arbitrary shape under two assumptions: with high probability, two vertices in the large subset are far from each other and have…

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…

Through this paper we analyze the ergodic properties of continuous time Markov chains with values on the one-dimensional spin lattice 1,...,d}^N (also known as the Bernoulli space). Initially, we consider as the infinitesimal generator the…

We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to…

This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…

Phylogenetic trees constitute an interesting class of objects for stochastic processes due to the non-standard nature of the space they inhabit. In particular, many statistical applications require the construction of Markov processes on…

The pre-image topological pressure is defined for bundle random dynamical systems. A variational principle for it has also been given.

We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the…

We show that, for every positive real number h and every positive integer p, there exist oriented graphs G, G' (with countably many vertices) that are strongly connected, of period p, of Gurevich entropy h, such that G is positive recurrent…

In this article we will apply complex projective metrics to sequences of complex transfer operators generated by Young towers, countable shifts and other types of distance expanding maps (possibly time dependent) with countable degrees. We…

Let $P^V_t$, $t\ge0$, be the Schrodinger semigroup associated to a potential $V$ and Markov semigroup $P_t$, $t\ge0$, on $C(X)$. Existence is established of a left eigenvector and right eigenvector corresponding to the spectral radius…