Boundary effects for KPZ universality in finite volume
Thèse
Lieu d'accueil :
Laboratoire de Physique Théorique, Toulouse
Contact :
Sylvain Prolhac (Toulouse)
Court résumé :
KPZ universality describes the dynamics of large scale fluctuations in
a variety of systems, such as growing interfaces or one-dimensional fluids. It
has become in the past few years a prominent topic at the interface between
non-equilibrium statistical physics (theory, numerics and experiments) and
probability theory (Markov processes, stochastic differential equations). At
the KPZ fixed point, the fundamental object of interest is a very singular
random function depending on space and time. Despite the existence of
some connections to random matrix theory obtained in the past twenty
years and verified in beautiful experiments, the nature of the KPZ fixed
point remains largely mysterious.
Building on recent progress about quasi-particle excitations in finite volume, the aim of this thesis will be to understand the effect of boundary conditions connecting the system to an external environment. A promising approach consists in large scale asymptotics of a simple Markov process called the totally asymmetric simple exclusion process (TASEP), which is exactly solvable using Bethe ansatz integrability. Another encouraging path, which deals with late time KPZ statistics directly in the continuum, is based on a recently discovered connection to extreme value statistics of Wiener processes.
a variety of systems, such as growing interfaces or one-dimensional fluids. It
has become in the past few years a prominent topic at the interface between
non-equilibrium statistical physics (theory, numerics and experiments) and
probability theory (Markov processes, stochastic differential equations). At
the KPZ fixed point, the fundamental object of interest is a very singular
random function depending on space and time. Despite the existence of
some connections to random matrix theory obtained in the past twenty
years and verified in beautiful experiments, the nature of the KPZ fixed
point remains largely mysterious.
Building on recent progress about quasi-particle excitations in finite volume, the aim of this thesis will be to understand the effect of boundary conditions connecting the system to an external environment. A promising approach consists in large scale asymptotics of a simple Markov process called the totally asymmetric simple exclusion process (TASEP), which is exactly solvable using Bethe ansatz integrability. Another encouraging path, which deals with late time KPZ statistics directly in the continuum, is based on a recently discovered connection to extreme value statistics of Wiener processes.
