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We investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a recently proposed approach to express the joint probability density of the particle position and of its multiple boundary local times via a multi-dimensional Laplace transform of the conventional propagator satisfying the diffusion equation with mixed Robin boundary conditions. In the particular cases of an interval, a circular annulus and a spherical shell, this representation can be explicitly inverted to access the statistics of two boundary local times. We provide the exact solutions and their probabilistic interpretation for the case of an interval and sketch their derivation for two other cases. We also obtain the distributions of various associated first-passage times and discuss their applications.
We study a stochastic process $X_t$ related to the Bessel and the Rayleigh processes, with various applications in physics, chemistry, biology, economics, finance and other fields. The stochastic differential equation is $dX_t = (nD/X_t) dt + sqrt{2D
In noisy environments such as the cell, many processes involve target sites that are often hidden or inactive, and thus not always available for reaction with diffusing entities. To understand reaction kinetics in these situations, we study the first
We investigate the voltage-driven transport of hybridized DNA through membrane channels. As membrane channels are typically too narrow to accommodate hybridized DNA, the dehybridization of the DNA is the critical rate limiting step in the transport p
With nontrivial entropy production, first passage process is one of the most common nonequilibrium process in stochastic thermodynamics. Using one dimensional birth and death precess as a model framework, approximated expressions of mean first passag
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 homogenisatio