In this review, we discuss the persistence and the related first-passage properties in
extended many-body nonequilibrium systems. Starting with simple systems with one or few …

We present a systematic study of the statistics of the occupation time and related random
variables for stochastic processes with independent intervals of time. According to the nature …

Dew is the condensation of water vapor into liquid droplets on a substrate. It is characterized
by an initial heterogeneous nucleation on a substrate and a further growth of droplets. The …

Heterogeneous diffusion with a spatially changing diffusion coefficient arises in many
experimental systems such as protein dynamics in the cell cytoplasm, mobility of cajal …

We investigate the nonergodic properties of blinking nanocrystals modeled by a Lévy-walk
stochastic process. Using a nonergodic mean field approach we calculate the distribution …

Abstract The'Arcsine'laws of Brownian particles in one dimension describe distributions of
three quantities: the time tm to reach maximum position, the time tr spent on the positive side …

Motivated by recent experimental observations of power-law statistics both in spectral
diffusion process and fluorescence intermittency of individual semiconductor nanocrystals …

We consider a system of N noncrossing Brownian particles in one dimension. We find the
exact rate function that describes the long-time large deviation statistics of their occupation …

Functionals of Brownian motion have diverse applications in physics, mathematics, and
other fields. The probability density function (PDF) of Brownian functionals satisfies the …

For weakly non ergodic systems, the probability density function of a time average
observable O is f_α(O)=-1\overπϵ→0Imj=1^Lp^eq_j(O-O_j+iϵ)^α-1\overj=1^Lp^eq_j(O …