Stochastic evolutions in continuum
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.