Related papers: Sign-changes as a universal concept in first-passa…
We develop a method based on martingales to study first-passage problems of time-additive observables exiting an interval of finite width in a Markov process. In the limit that the interval width is large, we derive generic expressions for…
Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widepsread. This deviation from brownian motion is usually characterized by a sublinear time dependence of the mean…
The first passage time (FPT) problem is studied for superstatistical models assuming that the mesoscopic system dynamics is described by a Fokker-Planck equation. We show that all moments of the random intensive parameter associated to the…
The counting function on binary values is extended to the signed case in order to count the number of transitions between contiguous locations. A generalized subdifferential for the sign change counting function is given where classical…
Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods…
The waiting time distribution has, in recent years, proven to be a useful statistical tool for characterising transport in nanoscale quantum transport. In particular, as opposed to moments of the distribution of transferred charge, which…
We present general methods to exactly calculate mean-first passage quantities on self-similar networks defined recursively. In particular, we calculate the mean first-passage time and the splitting probabilities associated to a source and…
First passage of stochastic processes under resetting has recently been an active research topic in the field of statistical physics. However, most of previous studies mainly focused on the systems with continuous time and space. In this…
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…
In this paper we study approximations for boundary crossing probabilities for the moving sums of i.i.d. normal random variables. We propose approximating a discrete time problem with a continuous time problem allowing us to apply developed…
We study the mean time for a random walk to traverse between two arbitrary sites of the Erdos-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as…
The general, multidimensional barrier crossing problem for diffusive processes under the action of conservative forces is studied with the goal of developing tractable approximations. Particular attention is given to the effect of different…
The graph transformation approach is a recently proposed method for computing mean first passage times, rates, and committor probabilities for kinetic transition networks. Here we compare the performance to existing linear algebra methods,…
First passage phenomena arise across physics, biology, and finance when stochastic processes first reach a threshold, triggering downstream events. Examples include the irreversible exit from a domain, a biochemical reaction, a financial…
Consider first passage percolation on $\mathbb{Z}^d$ with passage times given by i.i.d. random variables with common distribution $F$. Let $t_\pi(u,v)$ be the time from $u$ to $v$ for a path $\pi$ and $t(u,v)$ the minimal time among all…
We explore first-passage phenomenology for biased active processes with a renewal-type structure, focusing in particular on paradigmatic run-and-tumble models in both discrete and continuous state spaces. In general, we show there is no…
Current is a characteristic feature of nonequilibrium systems. In stochastic systems, these currents exhibit fluctuations constrained by the rate of dissipation in accordance with the recently discovered thermodynamic uncertainty relation.…
In first-passage percolation, one places nonnegative i.i.d. random variables (T(e)) on the edges of Z^d. A geodesic is an optimal path for the passage times T(e). Consider a local property of the time environment. We call it a pattern. We…
We consider first-passage percolation on the class of "high-dimensional" graphs that can be written as an iterated Cartesian product $G\square G \square \dots \square G$ of some base graph $G$ as the number of factors tends to infinity. We…
This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges can act as stochastic transports between two…