Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics
stripes SFB701

Project A5

Stochastic evolutions in continuum


Principal Investigator(s) Other Investigators
Yuri Kondratiev
José Luís da Silva
Benjamin Gess
Oleksandr Kutoviy
Tetyana Pasurek

Summary:

The main aim of the project is the study of Markov random processes on configuration spaces in continuum. We suppose to improve existing and to develop new methods for the construction of spatial birth-and-death processes, jumping particles random evolutions and diffusions of infinite particle systems. A special attention will be given to hydrodynamic limits of various stochastic evolutions in the continuum. In particular, we will consider scalings of fluctuations which should produce super-Brownian motions for the continuous contact model and for the voter model. We will analyze spectral properties of Markov generators and related ergodicity bounds for the non-equilibrium Glauber dynamics and for other classes of spatial birth-and-death processes. There will be considered applications to individual based models in spatial ecology, socio-economic models, classical and quantum continuous systems in statistical physics.

Recent Preprints:

17010 Kesten's bound for sub-exponential densities on the real line and its multi-dimensional analogues PDF | PS.GZ
17009 Accelerated front propagation for monostable equations with nonlocal diffusion PDF | PS.GZ
17008 The hair-trigger effect for a class of nonlocal nonlinear equations PDF | PS.GZ
17007 Global stability in a nonlocal reaction-diffusion equation PDF | PS.GZ
17004 An infinite dimensional umbral calculus PDF | PS.GZ
16026 Weak-coupling limit for ergodic environments PDF | PS.GZ
16019 Existence and uniqueness theorems for solutions of McKean-Vlasov stochastic equations PDF | PS.GZ
16018 Resolvent bounds for jump generators and ground state asymptotics for nonlocal Schrödinger operators PDF | PS.GZ
16014 Spectral analysis of non-local Schrödinger operators PDF | PS.GZ
16012 Fractional kinetic hierarchies and intermittency PDF | PS.GZ