Related papers: Long-time dynamics of stochastic differential equa…
In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient…
Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the…
We investigate the impact of hydrodynamic fluctuations on correlation functions in a scale invariant fluid with a conserved $U(1)$ charge. The kinetic equations for the two-point functions of pressure, momentum and heat energy densities are…
This review-type paper is based on a talk given at the conference {\'E}tats de la Recherche en M{\'e}canique statistique, which took place at IHP in Paris (December 10-14, 2018). We revisit old results from the 80's about one dimensional…
This text grew out of some lecture notes prepared by the author in the occasion of a series of three lectures during the workshop "Young mathematicians in dynamical systems" organized by Francoise Dal'bo, Louis Funar, Boris Hasselblatt and…
We begin herewith the editing of physics notes taken in the course of Journal Club seminars at INFN-LNF in 1996. The activity consists of informal talks about work in progress and/or review of (more or less) recent physics results of…
Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…
This paper studies stabilities of stochastic differential equation (SDE) driven by time-changed L\'evy noise in both probability and moment sense. This provides more flexibility in modeling schemes in application areas including physics,…
In this paper, we study the long-time behavior of full Ericksen-Leslie system modeling the hydrodynamics of nematic liquid crystals between two dimensional unit spheres. Under a weaker assumption for Leslie's coefficients, we give the key…
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.
These lecture notes are an extended version of my lectures on L\'evy and L\'evy-type (Feller) processes given at the "Second Barcelona Summer School on Stochastic Analysis" 2014 organized by the Centre de Recerca Matemaatica (CRM). The…
This document presents the contents of three lectures delivered by the author at the Erd\H{o}s Center School ``Optimal Transport on Quantum Structures'', Septemer 19-23, 2022 in Budapest, Hungary. It presents a fairly self contained account…
This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…
These are notes of lectures given at the Third School of Theoretical Physics in Jijel (Algeria, September 2009). The subject of these notes is differential geometry, complex and quaternionic structures with applications to theoretical…
These notes provide an introduction to and a survey on recent results about the long-time behaviour of solutions to hyperbolic partial differential equations with time-dependent coefficients. Particular emphasis is given also to questions…
We develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point (with respect to the Lebesgue measure) is asymptotically attracted to the origin with unit probability.…
This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis.
In these lecture notes we discuss recent progress in the rigorous derivation of effective evolution equations for the description of the dynamics of quantum mechanical many-body systems.
Elucidating the statistical properties of extreme meteo-climatic events and capturing the physical processes responsible for their occurrence are key steps for improving our understanding of climate variability and climate change and for…
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…