Following works of Furstenberg and Nevo and Zimmer we present an outline of a theory of stationary (or m-stationary) dynamical systems for a general acting group G equipped with a probability measure m. Our purpose is two-fold: First to suggest a more abstract line of development, including a simple structure theory. Second, to point out some interesting applications; one of these is a Szemeréd...

We investigate the nature of the dynamically inactive phase of a simple symmetric exclusion process on a ring. We find that as the system’s activity is tuned to a lower-than-average value the particles progressively lump into a single cluster, thereby forming a kink in the density profile. All dynamical regimes, and their finite size range of validity, are explicitly determined. ‡ vivien.lecomt...

We present a particle filter-based multitarget tracking method incorporating Gaussian process dynamical model (GPDM) to improve robustness in multitarget tracking. With the particle filter Gaussian process dynamical model (PFGPDM), a highdimensional target trajectory dataset of the observation space is projected to a low-dimensional latent space in a nonlinear probabilistic manner, which will t...

Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model. This dynamical model exhibits very interesting behavior. Our goal in this survey is to give an overview of the work in dynamical percolation that has been do...

One calls attention to the fact that the stochastic dynamic systems are not random completely. They have both random and regular components of their evolution. Determinitic dynamic system is considered to be a special case of dynamic system with vanishing stochastic component of evolution. Mathematical technique for description of regular evolution component of dynamic systems (stochastic and d...

We present a particle filter-based multitarget tracking method incorporating Gaussian process dynamical model (GPDM) to improve robustness in multitarget tracking. With the particle filter Gaussian process dynamical model (PFGPDM), a highdimensional target trajectory dataset of the observation space is projected to a low-dimensional latent space in a nonlinear probabilistic manner, which will t...