Poisson approximation has received extensive interest in recent probability literature. The general problem is to derive bounds on the closeness of a suitable Poisson distribution to the distribution in question (usually of discrete type). To measure the degree of proximity of Poisson approximation, the following distances are usually introduced: for any two random variables X and Y taking valu...

A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to random samples of two discrete distributions. Specifically, we estimate what we call the dissimilarity probability of a sample, i.e., the probability of a d...

This paper considers the class of discrete distributions for which the distribution function is a log-concave sequence. It is shown that such distributions arise from a wide variety of circumstances in Reliability, and that these have a decreasing reversed hazard rate. After examining the closures of the class under certain key operations, sharp upper and lower bounds on the reliability functio...

Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the nonequilibrium properties of a Fermi liquid. We apply an interaction quench within the Fermi liquid phase of the Hubbard model by switching on a weak interaction suddenly; then we follow the real-time dynamics of the momentum distributio...

The distribution of the number of trials until the first occurrence of consecutive k successes in Bernoulli trials with success probability p is called a geometric distribution of order k. This definition is due to Philippou, Georghiou and Philippou (1983). Though the distribution seems to have been interested since De Moivre (1667-1754)’s works (Todhunter (1865), Feller (1968), Johnson, Kotz a...

We study a one parameter family of discrete Löwner evolutions driven by a random walk on the real line. We show that it converges to the stochastic Löwner evolution (SLE) under rescaling. We show that the discrete Löwner evolution satisfies Markovian-type and symmetry properties analogous to SLE, and establish a phase transition property for the discrete Löwner evolution when the parameter equa...

In this paper the properties of node-node adjacency matrix in acyclic digraphs are considered. It is shown that topological ordering and node-node adjacency matrix are closely related. In fact, first the one to one correspondence between upper triangularity of node-node adjacency matrix and existence of directed cycles in digraphs is proved and then with this correspondence other properties of ...

The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially directed meaning that certain edges are directed and others are undirected. In the paper we define a configuration model for such networks where nodes have in-, ou...

We present a novel stochastic Petri net formalism where both discrete and continuous phase-type firing delays can appear simultaneously in the same model. By capturing non-Markovian behavior in discrete or continuous time, as appropriate, the formalism affords higher modeling fidelity. Alone, discrete or continuous phase-type Petri nets have simple underlying Markov chains, but mixing the two c...