objective of the project is to contribute (through the
development of mathematical tools for the study of
information theory in physics and statistics) to
strategic research related to the problems of
extraction, processing and protection of classical and
quantum information. We shall deal with three different,
but closely related topics.
The first group of problems concerns the Lempel–Ziv
coding algorithm whose performance studies have led to
deep insights into specific and relative entropies of
stationary measures on shift spaces. Notable among those
is the characterisation of the specific entropy of a
stochastic source in terms of the asymptotics of
recurrence times of a typical signal and the specific
cross entropy in terms of waiting times. We shall
investigate in depth the mathematical theory of entropic
estimators with emphasis on their fluctuations and
fractal dimension theory of the level sets.
The second group concerns bipartite systems with
infinitely many degrees of freedom. For those systems,
it is not clear what is a good measure of entanglement.
Recently, much progress has been made in the setting of
quantum fields on flat space, and computations in simple
models are starting to reveal mechanisms responsible for
geometric formulae for entanglement entropy.
Furthermore, there are proposals on how to give meaning
to information for subsystems such as a single wave. Our
goal is to develop more realistic models in relativistic
physics, with applications to QFT on AdS spaces and the
black hole information paradox.
The third group deals with fluid flows in a pipe. An
important question from the point of view of
applications is the estimation of viscosity using
long-time observations of the kinetic energy and
vorticity. This requires investigation of probabilistic
limit theorems for the observables and the expression of
resulting quantities in terms of viscosity. Our goal is
to find reliable estimators and to investigate their