Related papers: Cascade-free sequences, dispersion index, and stat…
We study a 1D system with a power-law quasiparticle dispersion $\propto |k|^\alpha\sign k$ in the presence of a short-range-correlated random potential and demonstrate that for $\alpha<1/2$ it exhibits a disorder-driven quantum phase…
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…
The paper studies the time-homogeneous two-state Markov chains; the states are assumed to be binary symbols 0 and 1. The higher-order absolute differences taken from progressive states of a given chain are considered. A discrete capacity of…
Let us consider a homogeneous Markov chain with discrete time and with a finite set of states $E_0,\ldots,E_n$ such that the state $E_0$ is absorbing, states $E_1,\ldots,E_n$ are nonrecurrent. The goal of this work is to study frequencies…
This paper describes a low-complexity approach for reconstructing average packet arrival rates and instantaneous packet counts at a router in a communication network, where the arrivals of packets in each flow follow a Poisson process.…
Let $I$ be an independent set drawn from the discrete $d$-dimensional hypercube $Q_d=\{0,1\}^d$ according to the hard-core distribution with parameter $\lambda>0$ (that is, the distribution in which each independent set $I$ is chosen with…
The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of N sites. It is partially asymmetric…
Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…
We propose a novel statistical inference methodology for multiway count data that is corrupted by false zeros that are indistinguishable from true zero counts. Our approach consists of zero-truncating the Poisson distribution to neglect all…
This paper uses the generator comparison approach of Stein's method to analyze the gap between steady-state distributions of Markov chains and diffusion processes. The "standard" generator comparison approach starts with the Poisson…
Finite-state dimension quantifies the asymptotic rate of information in an infinite sequence as perceived by finite automata. For a fixed alphabet, the infinite sequences that have maximal finite-state dimension are exactly those that are…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…
This work presents an exact microcanonical combinatorial analysis of the one-dimensional antiferromagnetic Ising model. At the primary ground-state level crossing $B/J=2$, degeneracies follow the Fibonacci and Lucas sequences for open…
The $(d,\alpha,\beta,\gamma)$-branching particle system consists of particles moving in $R^d$ according to a symmetric $\alpha$-stable L\'evy process $(0<\alpha\leq 2)$, splitting with a critical $(1+\beta)$-branching law $(0<\beta\leq 1)$,…
We consider random permutations on $\Sn$ with logarithmic growing cycles weights and study asymptotic behavior as the length $n$ tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In our model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
Real count data time series often show the phenomenon of the underdispersion and overdispersion. In this paper, we develop two extensions of the first-order integer-valued autoregressive process with Poisson innovations, based on binomial…
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 suggest a protocol for perfect quantum communication through spin chain channels. By combining a dual-rail encoding with measurements only at the receiving end, we can get conclusively perfect state transfer, whose probability of success…
Let $\chi$ be a Dirichlet character mod $D$ with $L(s,\chi)$ its associated $L$-function, and let $\psi(x,q,a)$ be, as usual, Chebyshev's prime-counting function for the primes of the arithmetic progression $a$ (mod $q$) with $(a,q)=1$. For…