Related papers: Exact calculations of first-passage quantities on …
A collection of identical and independent rare event first passage times is considered. The problem of finding the fastest out of $N$ such events to occur is called an extreme first passage time. The rare event times are singular and limit…
We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modeled as a two state model; the particle moves with a constant propulsion strength…
In this paper, we consider a homogeneous Markov process \xi(t;\omega) on an ultrametric space Q_p, with distribution density f(x,t), x in Q_p, t in R_+, satisfying the ultrametric diffusion equation df(x,t)/dt =-Df(x,t). We construct and…
We consider a run-and-tumble particle (RTP) in one dimension, subjected to a telegraphic noise with a constant rate $\gamma$, and in the presence of an external confining potential $V(x) = \alpha |x|^p$ with $p \geq 1$. We compute the mean…
We study the transport of many partially distinguishable and possibly interacting particles under the action of repeated projective measurements on a target space and investigate how the particles' interference affects the mean first…
In this work we propose a novel method to calculate mean first-passage times (MFPTs) for random walks on graphs, based on a dimensionality reduction technique for Markov State Models, known as local-equilibrium (LE). We show that for a…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…
Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…
The time it takes the fastest searcher out of $N\gg1$ searchers to find a target determines the timescale of many physical, chemical, and biological processes. This time is called an extreme first passage time (FPT) and is typically much…
In adaptive networks fragmentation transitions have been observed in which the network breaks into disconnected components. We present an analytical approach for calculating the transition point in general adaptive network models. Using the…
In this paper, we are concerned with mean hitting time $\langle\mathcal{H}\rangle$ for random walks on recursive growth tree networks that are built based on an arbitrary tree as the seed via implementing various primitive graphic…
Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations…
First-passage times are often the most relevant aspect of a complex Markovian network, because they signify when information processing has resulted in a definite decision. Previous studies have shown that for kinetic proofreading networks…
We study first passage percolation on the configuration model (CM) having power-law degrees with exponent $\tau\in [1,2)$. To this end we equip the edges with exponential weights. We derive the distributional limit of the minimal weight of…
We consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations on $\mathbb{Z}^d$, $d\geq 2$, including discrete Gaussian free fields, Ginzburg-Landau $\nabla \phi$…
Motivated by the dynamics of resonant neurons we consider a differentiable, non-Markovian random process $x(t)$ and particularly the time after which it will reach a certain level $x_b$. The probability density of this first passage time is…
The poster presents an analytic formalism describing metric properties of undirected random graphs with arbitrary degree distributions and statistically uncorrelated (i.e. randomly connected) vertices. The formalism allows to calculate the…
The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
This paper introduces a new way to define a genome rearrangement distance, using the concept of mean first passage time from probability theory. Crucially, this distance estimate provides a genuine metric on genome space. We develop the…