Related papers: The mean shape of transition and first-passage pat…
Many transport processes in ecology, physics and biochemistry can be described by the average time to first find a site or exit a region, starting from an initial position. Typical mathematical treatments are based on formulations that…
We extend the random walk framework to include compounded steps, providing first-passage time (FPT) properties for a new class of superdiffusive processes, which are governed by the space-fractional spectral Fokker-Planck equation. This…
We consider a Markovian jumping process with two absorbing barriers, for which the waiting-time distribution involves a position-dependent coefficient. We solve the Fokker-Planck equation with boundary conditions and calculate the mean…
We consider a run-and-tumble particle on a half-line with an absorbing target at the origin. The particle has an internal velocity state that switches between two opposite values at Poisson-distributed times. The position of the particle…
We derive an approximate but fully explicit formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape in a general elongated domain in the plane. Our approximation combines conformal mapping, boundary…
We study the statistics of the first passage of a random walker to absorbing subsets of the boundary of compact domains in different spatial dimensions. We describe a novel diagnostic method to quantify the trajectory-to-trajectory…
Biomolecular conformational transitions are usually modeled as barrier crossings in a free energy landscape. The transition paths connect two local free energy minima and transition path times (TPT) are the actual durations of the crossing…
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…
In this paper, we consider the problem of mean first-passage time (MFPT) in quantum mechanics; the MFPT is the average time of the transition from a given initial state, passing through some intermediate states, to a given final state for…
We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we…
We consider the quantum first detection problem for a particle evolving on a graph under repeated projective measurements with fixed rate $1/\tau$. A general formula for the mean first detected transition time is obtained for a quantum walk…
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…
Using a novel theoretical approach, we study the mean first encounter time (MFET) between the two ends of a polymer. Previous approaches used various simplifications that reduced the complexity of the problem, leading, however to…
We investigate some simple and surprising properties of a one-dimensional Brownian trajectory with diffusion coefficient $D$ that starts at the origin and reaches $X$ either: (i) at time $T$ or (ii) for the first time at time $T$. We…
We derive a general exact formula for the mean first passage time (MFPT) from a fixed point inside a planar domain to an escape region on its boundary. The underlying mixed Dirichlet-Neumann boundary value problem is conformally mapped onto…
The first passage is a generic concept for quantifying when a random quantity such as the position of a diffusing molecule or the value of a stock crosses a preset threshold (target) for the first time. The last decade saw an enlightening…
Recently, the thermodynamics and kinetics of black hole phase transitions have garnered attention, particularly with the black hole radius being utilized as an order parameter within a generalized free energy landscape. In this framework,…
Transition paths are rare events occurring when a system, thanks to the effect of fluctuations, crosses successfully from one stable state to another by surmounting an energy barrier. Even though they are of great significance in many…
The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study…
The computation of the probability of the first-passage time through a given threshold of a stochastic process is a classic problem that appears in many branches of physics. When the stochastic dynamics is markovian, the probability admits…