We study the statistics of random functionals Z=∫ 0 T [x (t)] γ− 2 dt, where x (t) is the
trajectory of a one-dimensional Brownian motion with diffusion constant D under the effect of …

A lattice random walk is a mathematical representation of movement through random steps
on a lattice at discrete times. It is commonly referred to as Pólya's walk when the steps occur …

The infimum of an integrated current is its extreme value against the direction of its average
flow. Using martingale theory, we show that the infima of integrated edge currents in time …

Recently observation of random walks in complex environments like the cell and other
glassy systems revealed that the spreading of particles, at its tails, follows a spatial …

We present a spectral-theoretic approach to time-average statistical mechanics for general,
nonequilibrium initial conditions. We consider the statistics of bounded, local additive …

First passage time (FPT) theory is often used to estimate timescales in cellular and
molecular biology. While the overwhelming majority of studies have focused on the time it …

We investigate a class of diffusion-controlled reactions that are initiated at the time instance
when a prescribed number K among N particles independently diffusing in a solvent are …

We derive general bounds on the probability that the empirical first-passage time τ¯ n≡∑ i=
1 n τ i/n of a reversible ergodic Markov process inferred from a sample of n independent …

A variety of systems in physics, chemistry, biology, and psychology are modeled in terms of
diffusing'searchers' looking for'targets'. Examples range from gene regulation, to cell …

We illuminate the many-body effects underlying the structure, formation, and dissolution of
cellular adhesion domains in the presence and absence of forces. We consider mixed …