Related papers: Selected problems in probability theory
Given a finite sequence of events and a well-defined notion of events being interesting, the Odds-theorem (Bruss (2000)) gives an online strategy to stop on the last interesting event. It is optimal for independent events. Here we study…
We obtain expected number of arrivals, absorption probabilities and expected time before absorption for a discrete random walk on the integers with an infinite set of equidistant multiple function barriers
A Lindley process arises from classical studies in queueing theory and it usually reflects waiting times of customers in single server models. In this note we study recurrence of its higher dimensional counterpart under some mild…
We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…
In this paper we review some general properties of probability distributions which exibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of…
In this note we briefly survey and propose some open problems related to isoparametric theory.
In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.
The problems of enumerating lattice walks, with an arbitrary finite set of allowed steps, both in one and two dimensions, where one must always stay in the non-negative half-line and quarter-plane respectively, are used, as case studies, to…
We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided…
On the complete graph ${\cal{K}}_M$ with $M \ge3$ vertices consider two independent discrete time random walks $\mathbb{X}$ and $\mathbb{Y}$, choosing their steps uniformly at random. A pair of trajectories $\mathbb{X} = \{ X_1, X_2, \dots…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
Two closely related discrete probability distributions are introduced. In each case the support is a set of vectors in $\mathbb{R}^n$ obtained from the partitions of the fixed positive integer $n$. These distributions arise naturally when…
By analogy with Carleson's observation on Cardy's formula describing crossing probabilities for the scaling limit of critical percolation, we exhibit ``privileged geometries'' for Stochastic Loewner Evolutions with various parameters, for…
We study the motion of a particle on the two-dimensional honeycomb lattice, whose sites are occupied by either flipping rotators or flipping mirrors, which scatter the particle according to a deterministic rule. For both types of scatterers…
We introduce a lattice random walk discretisation scheme for stochastic differential equations (SDEs) that samples binary or ternary increments at each step, suppressing complex drift and diffusion computations to simple 1 or 2 bit random…
Discrete differential equations appear most prominently in planar map and lattice path enumeration. In this work we consider discrete differential equations with an additional parameter $x$, where the order of the equation is $1$ for $x=0$…
For covering spaces and properly discontinuous actions with compatible diffusion processes, we discuss Lyons-Sullivan discretizations of the processes and the associated function theory.
We investigate the first passage time t_{j,N} to a given chemical or Euclidean distance of the first j of a set of N>>1 independent random walkers all initially placed on a site of a disordered medium. To solve this order-statistics problem…