Speaker
Description
The configuration space U(X) over a base space X is the space
of all locally finite point measures on X. The space U(X) being equipped
with the vague topology, the L^2-transportation distance and a point
process, it is a Polish extended metric measure space. In this talk, we
show that U(X), equipped with the Poisson point process, satisfies
synthetic lower Ricci curvature bounds if and only if so does X. As a
byproduct, we obtain the Sobolev-to-Lipschitz property on U(X), which
confirms the conjecture by Röckner-Schied (J. Funct. Anal. '99). We
discuss several applications to the corresponding infinite-particle
systems such as the integral Varadhan short-time asymptotic of the heat
flow on U(X) and a new characterisation of ergodicity of particle
systems in terms of the L^2-transportation distance. If time allows, we
also explain the case beyond the Poisson point process. This talk is
based on the joint work with Lorenzo Dello Schiavo (Institute of Science
and Technology Austria).
