The theory of large deviations is concerned with the exponential decay of probabilities of
large fluctuations in random systems. These probabilities are important in many fields of …

We consider the problem of conditioning a Markov process on a rare event and of
representing this conditioned process by a conditioning-free process, called the effective or …

We provide here a brief perspective on the glass transition field. It is an assessment, written
from the point of view of theory, of where the field is and where it seems to be heading. We …

We show that the dynamics of kinetically constrained models of glass formers takes place at
a first-order coexistence line between active and inactive dynamical phases. We prove this …

We investigate the dynamics of kinetically constrained models of glass formers by analysing
the statistics of trajectories of the dynamics, or histories, using large deviation function …

These notes give a summary of techniques used in large deviation theory to study the
fluctuations of time-additive quantities, called dynamical observables, defined in the context …

Relative fluctuations of observables in discrete stochastic systems are bounded at all times
by the mean dynamical activity in the system, quantified by the mean number of jumps. This …

Understanding current fluctuations is of fundamental importance and paves the way for the
development of practical applications. According to the thermodynamic and kinetic …

The thermodynamic formalism allows one to access the chaotic properties of equilibrium
and out-of-equilibrium systems, by deriving those from a dynamical partition function. The …

Many natural and engineered dynamical systems, including all living objects, exhibit
signatures of what can be called spontaneous dynamical long-range order (DLRO). This …