Related papers: $p$-adic boundary laws and Markov chains on trees

Bounded infinite graphs are defined on the basis of natural physical requirements. When specialized to trees this definition leads to a natural conjecture that the average connectivity dimension of bounded trees cannot exceed two. We verify…

We consider a Markov chain $\{X_n\}_{n=0}^\8$ on $\R^d$ defined by the stochastic recursion $X_{n}=M_n X_{n-1}+Q_n$, where $(Q_n,M_n)$ are i.i.d. random variables taking values in the affine group $H=\R^d\rtimes {\rm GL}(\R^d)$. Assume that…

The extremes of a univariate Markov chain with regulary varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper, we extend…

Let $p$ be a fixed prime number, and $q$ a power of $p$. For any curve over $\mathbb{F}_q$ and any local system on it, we have a number field generated by the traces of Frobenii at closed points, known as the trace field. We show that as we…

Cascades on random networks are typically analyzed by assuming they map onto percolation processes and then are solved using generating function formulations. This approach assumes that the network is infinite and weakly connected, yet…

We introduce quantum Markov states (QMS) in a general tree graph $G= (V, E)$, extending the Cayley tree's case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of this paper concerns the…

Let $G$ be an infinite graph such that each tree in the wired uniform spanning forest on $G$ has one end almost surely. On such graphs $G$, we give a family of continuous, measure preserving, almost one-to-one mappings from the wired…

The paper introduces a Poisson-type problem on a mixed-dimensional structure combining a Euclidean domain and a lower-dimensional self-similar component touching a compact surface (interface). The lower-dimensional piece is a so-called…

We prove dynamical local limits for the singular numbers of $p$-adic random matrix products at both the bulk and edge. The limit object which we construct, the reflecting Poisson sea, may thus be viewed as a $p$-adic analogue of line…

Stochastic gene regulatory networks with bursting dynamics can be modeled mesocopically as a generalized density-dependent Markov chain (GDDMC) or macroscopically as a piecewise-deterministic Markov process (PDMP). Here we prove a limit…

This paper is a survey of various proofs of the so called {\em fundamental theorem of Markov chains}: every ergodic Markov chain has a unique positive stationary distribution and the chain attains this distribution in the limit independent…

Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…

The Poisson boundary of a finite direct product of affine automorphism groups of homogeneous trees is considered. The Poisson boundary is shown to be a product of ends of trees with a hitting measure for spread-out, aperiodic measures of…

We introduce block Markov chains (BMCs) indexed by an infinite rooted tree. It turns out that BMCs define a new class of tree-indexed Markovian processes. We clarify the structure of BMCs in connection with Markov chains (MCs) and Markov…

We consider metrics which are preserved under a $p$-Wasserstein transport map, up to a possible contraction. In the case $p=1$ this corresponds to a metric which is uniformly curved in the sense of coarse Ricci curvature. We investigate the…

We give a unified treatment of the limit, as the size tends to infinity, of simply generated random trees, including both the well-known result in the standard case of critical Galton--Watson trees and similar but less well-known results in…

We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…

Consider the continuous-time Markov Branching Process. In critical case we consider a situation when the generating function of intensity of transformation of particles has the infinite second moment, but its tail regularly varies in sense…

In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains…

Perturbation theory for Markov chains addresses the question how small differences in the transitions of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the…