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Understanding the effect of disorder on critical phenomena is a
central issue in statistical mechanics. In probabilistic terms:
what happens if we perturb a system exhibiting a phase transition
by introducing a random environment? The physics community has
approached this very broad question by aiming at general criteria
that tell whether or not the addition of disorder changes the
critical properties of a model: some of the predictions are truly
striking and mathematically challenging. We approach this domain of
ideas by focusing on a specific class of models, the "pinning
models," for which a series of recent mathematical works has
essentially put all the main predictions of the physics community
on firm footing; in some cases, mathematicians have even gone
beyond, settling a number of controversial issues. But the purpose
of these notes, beyond treating the pinning models in full detail,
is also to convey the gist, or at least the flavor, of the "overall
picture," which is, in many respects, unfamiliar territory for
mathematicians.
Stemming from the IHP trimester "Stochastic Dynamics Out of
Equilibrium", this collection of contributions focuses on aspects
of nonequilibrium dynamics and its ongoing developments. It is
common practice in statistical mechanics to use models of large
interacting assemblies governed by stochastic dynamics. In this
context "equilibrium" is understood as stochastically (time)
reversible dynamics with respect to a prescribed Gibbs measure.
Nonequilibrium dynamics correspond on the other hand to
irreversible evolutions, where fluxes appear in physical systems,
and steady-state measures are unknown. The trimester, held at the
Institut Henri Poincare (IHP) in Paris from April to July 2017,
comprised various events relating to three domains (i) transport in
non-equilibrium statistical mechanics; (ii) the design of more
efficient simulation methods; (iii) life sciences. It brought
together physicists, mathematicians from many domains, computer
scientists, as well as researchers working at the interface between
biology, physics and mathematics. The present volume is
indispensable reading for researchers and Ph.D. students working in
such areas.
Stemming from the IHP trimester "Stochastic Dynamics Out of
Equilibrium", this collection of contributions focuses on aspects
of nonequilibrium dynamics and its ongoing developments. It is
common practice in statistical mechanics to use models of large
interacting assemblies governed by stochastic dynamics. In this
context "equilibrium" is understood as stochastically (time)
reversible dynamics with respect to a prescribed Gibbs measure.
Nonequilibrium dynamics correspond on the other hand to
irreversible evolutions, where fluxes appear in physical systems,
and steady-state measures are unknown. The trimester, held at the
Institut Henri Poincare (IHP) in Paris from April to July 2017,
comprised various events relating to three domains (i) transport in
non-equilibrium statistical mechanics; (ii) the design of more
efficient simulation methods; (iii) life sciences. It brought
together physicists, mathematicians from many domains, computer
scientists, as well as researchers working at the interface between
biology, physics and mathematics. The present volume is
indispensable reading for researchers and Ph.D. students working in
such areas.
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