Based on lectures given by one of the authors with many years of experience in teaching
stochastic processes, this textbook is unique in combining basic mathematical and physical …

Condensation phenomena arise through a collective behaviour of particles. They are
observed in both classical and quantum systems, ranging from the formation of traffic jams in …

Condensation is the phenomenon whereby one of a sum of random variables contributes a
finite fraction to the sum. It is manifested as an aggregation phenomenon in diverse physical …

A class of microscopic stochastic models is proposed to describe 1D pedestrian trajectories
obtained in laboratory experiments. The class contains continuous first-order models that …

We discuss the phase transition and critical exponents in the random allocation model (urn
model) for different statistical ensembles. We provide a unified presentation of the statistical …

Optimal velocity (OV) car-following models give with few parameters stable stop-and-go
waves propagating like in empirical data. Unfortunately, classical OV models locally oscillate …

We study the factorized steady state of a general class of mass transport models in which
mass, a conserved quantity, is transferred stochastically between sites. Condensation in …

Real space condensation is known to occur in stochastic models of mass transport in the
regime in which the globally conserved mass density is greater than a critical value. It has …

We study zero-range processes which are known to exhibit a condensation transition, where
above a critical density a non-zero fraction of all particles accumulates on a single lattice …

The paper presents the main aspects of a stochastic conservative model of the evolution of
the number of vehicles per road section. The model, defined in continuous time on a discrete …