Related papers: Formulas for Joint Probabilities for the Asymmetri…
We give an exact expression for the distribution of the position X(t) of a single second class particle in the asymmetric simple exclusion process (ASEP) where initially the second class particle is located at the origin and the first class…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…
A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In…
Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these…
In this paper we give a simple, short, and self-contained proof for a non-trivial upper bound on the probability that a random $\pm 1$ symmetric matrix is singular.
In this paper, we consider the two-species asymmetric simple exclusion process consisting of $N-1$ first-class particles and one second-class particle. We assume that the second-class particle is the rightmost particle at t=0. We provide an…
We derive the formula for the stationary states of particle-number conserving exclusion processes infinitesimally perturbed by inhomogeneous adsorption and desorption. The formula not only proves but also generalises the conjecture proposed…
In this paper we analyze the steady state of the Asymmetric Simple Exclusion process with open boundaries and second class particles by deforming it through the introduction of spectral parameters. The (unnormalized) probabilities of the…
Reliability of safety-critical systems is an important issue in system engineering and in most practical situations the reliability of a non series-parallel network system has to be calculated. Some methods for calculating reliability use…
We offer some summation formulas that appear to have great utility in probability theory. The proofs require some recent results from analysis that have thus far been applied to basic hypergeometric functions.
We prove Gaussian tail estimates for the transition probability of $n$ particles evolving as symmetric exclusion processes on $\bb Z^d$, improving results obtained in \cite{l}. We derive from this result a non-equilibrium Boltzmann-Gibbs…
Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong…
Sampling formulas describe probability laws of exchangeable combinatorial structures like partitions and compositions. We give a brief account of two known parametric families of sampling formulas and add a new family to the list.
In this paper we find explicit formulas for: (1) Green's function for a system of one-dimensional bosons interacting via a delta-function potential with particles confined to the positive half-line; and (2) the transition probability for…
In this pedagogical text aimed at those wanting to start thinking about or brush up on probabilistic inference, I review the rules by which probability distribution functions can (and cannot) be combined. I connect these rules to the…
Implicit particle filters for data assimilation update the particles by first choosing probabilities and then looking for particle locations that assume them, guiding the particles one by one to the high probability domain. We provide a…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. This permutation processes can…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
A traffic model on an open one-dimensional lattice is considered. At any discrete time moment, with prescribed probability, a particle arrives to the leftmost cell of the lattice, and, with prescribed probability, the arriving particle…