Related papers: The frequency of pattern occurrence in random walk…
In the last decade a huge amount of articles has been published studying pattern avoidance on permutations. From the point of view of enumeration, typically one tries to count permutations avoiding certain patterns according to their…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
Random walks are a series of up, down, and level steps that enumerate distinct paths from $(0,0)$ to $(2n,0)$, where $n$ is the semi-length of the path. We used these paths to analyze Catalan, Schr\"{o}der, and Motzkin number sequences…
Activities such as the movement of passengers and goods, the transfer of physical or digital assets, web navigation and even successive passes in football, result in timestamped paths through a physical or virtual network. The need to…
The movement of pedestrians is supposed to show certain regularities which can be best described by an ``algorithm'' for the individual behavior and is easily simulated on computers. This behavior is assumed to be determined by an intended…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
We study a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i)…
We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed $v_P$. We give upper bounds on the quenched probability that at…
Associated to a random walk on $\mathbb{Z}$ and a positive integer $n$, there is a return probability of the random walk returning to the origin after $n$ steps. An interesting question is when the set of return probabilities uniquely…
Ordinal data analysis is an interesting direction in machine learning. It mainly deals with data for which only the relationships `$<$', `$=$', `$>$' between pairs of points are known. We do an attempt of formalizing structures behind…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…
Nodes can be ranked according to their relative importance within the network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
We consider a recurrent random walk in random environment on a regular tree. Under suitable general assumptions upon the distribution of the environment, we show that the walk exhibits an unusual slow movement: the order of magnitude of the…
We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…
We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…
While records and order statistics of independent and identically distributed (i.i.d.) random variables X_1, ..., X_N are fully understood, much less is known for strongly correlated random variables, which is often the situation…
A rotor configuration on a graph contains in every vertex an infinite ordered sequence of rotors, each is pointing to a neighbor of the vertex. After sampling a configuration according to some probability measure, a rotor walk is a…
We ask if it is possible to find some particular continuous paths of unit length in linear Brownian motion. Beginning with a discrete version of the problem, we derive the asymptotics of the expected waiting time for several interesting…