Il sesto problema di Hilbert e le moderne teorie cinetiche.
In questo contributo si discute qualche problema connesso alla derivazione delle equazioni cinetiche a partire dalla meccanica dei sistemi di particelle.
In questo contributo si discute qualche problema connesso alla derivazione delle equazioni cinetiche a partire dalla meccanica dei sistemi di particelle.
We focus on invariant measures of an interacting particle system in the case when the set of sites, on which the particles move, has a structure different from the usually considered set . We have chosen the tree structure with the dynamics that leads to one of the classical particle systems, called the zero range process. The zero range process with the constant speed function corresponds to an infinite system of queues and the arrangement of servers in the tree structure is natural in a number...
In this paper, we prove that the laws of interacting brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.
In this paper, we prove that the laws of interacting Brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of Hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to Brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.
When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of conjugacy classes of the unitary group, using a dynamical rule inspired by the RSK algorithm. Our motivation for doing this is to develop a parallel programme, on the circle, to some recently discovered connections in random matrix theory between reflected and conditioned...