Related papers: Narrow-escape-time problem: the imperfect trapping…
After the review by Hauge and Stovneng the old question of "How long does it take to tunnel through the barrier?" has not still lost its relevance. As before, there is no clear answer to this question even for the one-dimensional completed…
The mean first exit (passage) time characterizes the average time of a stochastic process never leaving a fixed region in the state space, while the escape probability describes the likelihood of a transition from one region to another for…
Quantum escape of a particle via a time-dependent confining potential in a semi-infinite one-dimensional space is discussed. We describe the time-evolution of escape states in terms of scattering states of the quantum open system, and…
We perform computer simulations to explore the escape dynamics of a self-propelled (active) nanorod from circular confinements with narrow opening(s). Our results clearly demonstrate how the persistent and directed motion of the nanorod…
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…
The All-Pairs Max-Flow problem has gained significant popularity in the last two decades, and many results are known regarding its fine-grained complexity. Despite this, wide gaps remain in our understanding of the time complexity for…
What is the path associated with the fastest Brownian particle that reaches a narrow window located on the boundary of a domain? Although the distribution of the fastest arrival times has been well studied in dimension 1, much less is known…
We study the first passage time for a polymer, that we call the narrow encounter time (NETP), to reach a small target located on the surface of a microdomain. The polymer is modeled as a Freely Joint Chain (beads connected by springs with a…
We investigate how confinement may drastically change both the probability density of the first-encounter time and the related survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we…
The facilitated simple exclusion process (FEP) is a one-dimensional exclusion process with a dynamical constraint. We establish bounds on the mixing time of the FEP on the segment, with closed boundaries, and the circle. The FEP on these…
This paper proposes a universal microscopic model for the shallow confinement regime of single-electron tunneling devices. We consider particle escape from a quantum well generically emerging as a bifurcation in a smooth electrostatic…
We study an optimal investment problem with multiple entries and forced exits. A closed form solution of the optimisation problem is presented for general underlying diffusion dynamics and a general running payoff function in the case when…
The study of discrete-time stochastic processes on the half-line with mean drift at $x$ given by $\mu_1 (x) \to 0$ as $x \to \infty$ is known as Lamperti's problem. We give sharp almost-sure bounds for processes of this type in the case…
The first passage search of a diffusing target (prey) by multiple searchers (predators) in confinement is an important problem in the stochastic process literature. While the analogous problem in open space has been studied in some details,…
A fundamental issue in the analysis of emergency call centers is to estimate the time needed to return to a congestion-free regime after an unusual event with a massive arrival of calls. Call centers can generally be represented by timed…
For the enhancement of the transient stability of power systems, the key is to define a quantitative optimization formulation with system parameters as decision variables. In this paper, we model the disturbances by Gaussian noise and…
We study mixing times of the symmetric and asymmetric simple exclusion process on the segment where particles are allowed to enter and exit at the endpoints. We consider different regimes depending on the entering and exiting rates as well…
This paper focuses on the escape problem of a harmonically-forced classical particle from a purely-quartic truncated potential well. The latter corresponds to various engineering systems that involve purely cubic restoring force and absence…
In this paper we analyze the narrow capture problem for a single Brownian particle diffusing in a three-dimensional (3D) bounded domain containing a set of small, spherical traps. The boundary surface of each trap is taken to be a…
The trapping problem on graph (or network) as a typical focus of great interest has attracted more attention from various science fields, including applied mathematics and theoretical computer science, in the past. Here, we first study this…