Related papers: Selected problems in probability theory
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
We summarize some of the recent developments which link certain problems in combinatorial theory related to random growth to random matrix theory.
We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,infinity) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided…
In this article, the exponentiated discrete Lindley distribution is presented and studied. Some important distributional properties are discussed. Using the maximum likelihood method, estimation of the model parameters is investigated.…
We consider importance sampling for estimating the probability that a light-tailed $d$-dimensional random walk exits through one of many disjoint rare-event regions before reaching an anticipated target. This problem arises in sequential…
For some m \ge 4, let us color each column of the integer lattice L = Z^2 independently and uniformly into one of m colors. We do the same for the rows, independently from the columns. A point of L will be called blocked if its row and…
We investigate analytically and numerically the statistical properties of a random walk model with delayed transition probability dependence (delayed random walk). The characteristic feature of such a model is the oscillatory behavior of…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
A tempered version of the discrete Linnik distribution is introduced in order to obtain integer-valued distribution families connected to stable laws. The proposal constitutes a generalization of the well-known Poisson-Tweedie law, which is…
A variation of Rosenstock's trapping model in which $N$ independent random walkers are all initially placed upon a site of a one-dimensional lattice in the presence of a {\em one-sided} random distribution (with probability $c$) of…
Contrary to the theory of Markov processes, no general theory exists for the so called nonlinear Markov processes. We study an example of "nonlinear Markov process" related to classical probability theory, merely to random walks. This model…
This paper deals with the probabilistic behaviours of distributed systems described by a process calculus considering both probabilistic internal choices and nondeterministic external choices. For this calculus we define and study a typing…
In this review, an outline of the so called Freidlin-Wentzell theory and its recent extensions is given. Broadly, this theory studies the exponential rate at which the probabilities of rare events related to random perturbation of ODE…
The problem of missing link prediction in complex networks has attracted much attention recently. Two difficulties in link prediction are the sparsity and huge size of the target networks. Therefore, the design of an efficient and effective…
We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
This paper contains a selection, dictated by personal taste and by no means complete, of open problems in local discrete holomorphic dynamics.
The goal of this short note is to provide simple proofs for the "folklore facts" on the sample complexity of learning a discrete probability distribution over a known domain of size $k$ to various distances $\varepsilon$, with error…
In this article, we study special points of a simple random walk and a Gaussian free field, such as (nearly) favorite points, late points and high points. In section $2$, we extend results of [19] and suggest open problems for $d=2$. In…