A two days workshop to explore the connections of rough path theory with other fields of mathematics and theoretical physics including stochastic analysis, ergodicity of random dynamical systems, numerical integration methods, Hopf algebras and renormalization in quantum field theory.

Invited speakers

• Thomas Cass
• Aurelien Deya
• Peter Friz
• Loïc Foissy
• Martin Hairer
• Dominique Manchon
• József Lörinczi
• David Nualart
• Vincent Rivasseau
• Josef Teichmann
• Arnulf Jentzen

Informations

For further informations please contact Massimiliano Gubinelli (name.surname@dauphine.fr)

Supported by: ANR (project ECRU), CNRS, Institut Henri Poincaré.

Poster (pdf)

Program

Abstracts

Thomas Cass (Oxford University)

Evolving communities with individual preferences.

We consider a community of interacting individuals, each individual having preferences described by some probability measure on rough paths. For certain types of interaction we consider the problem of existence and uniqueness of some forward evolution, which accounts for the individuals preference, and correctly models the interaction with the aggregate behaviour of the community. The evolution of the population need not be governed by any over-arching PDE, but in the case where it is one can match the standard non-linear parabolic PDEs of McKean-Vlasov type with specific examples of communities. Rough paths continuity statements allows for straight forward analysis of propagation of chaos phenomena and large deviations.

Martin Hairer (Warwick University and Courant Institute)

Ergodic theory of non-Markovian stochastic processes

Abstract: We consider evolution equations driven by a noise that is not white in time, so that the resulting process does not have the Markov property. We show that there is an analogue in this setting to the usual Doob-Khashminski ergodicity criterion, provided that the driving noise satisfies a certain "quasi-Markov" property. This can be verified in many cases, including SDEs driven by fractional Brownian motion and thus having long-range memory.

Vincent Rivasseau (LPT, Universite Paris Sud)

The Loop Vertex Expansion

The loop vertex expansion is a recent substitute for cluster expansions which allows to compute connected functions of statistical mechanics or quantum field theory models without having to divide space into a (non-canonical) lattice. It might be of interest in the study of random walks and of concrete interacting models of rough paths.