Ergodicity of Non-equilibrium Glauber Dynamics in Continuum
نویسندگان
چکیده
We study asymptotic properties of the continuous Glauber dynamics with unbounded death and constant birth rates. In particular, an information about the spectrum location for the symbol of the Markov generator is obtained. The latter fact is used for the proof of the ergodicity of this process. We show that the speed of convergence to the equilibrium is exponential.
منابع مشابه
A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs
We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove...
متن کاملSurfaces of Constant Temperature for Glauber Dynamics
The wavefunction of a single spin system in a prepared initial state evolves to equilibrium with a heat bath. The average spin q(t) = p↑(t)− p↓(t) exhibits a characteristic time for this evolution. With the proper choice of spin flip rates, a dynamical Ising model (Glauber) can be constructed with the same characteristic time for transition of the average spin to equilibrium. The Glauber dynami...
متن کاملStochastic games with infinitely many interacting agents
We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove...
متن کاملRelaxation to equilibrium for two
We consider Glauber{type dynamics for two dimensional disordered magnets of Ising type. We prove that, if in equilibrium the disorder{averaged innuence of the boundary condition is suuciently small, then the corresponding Glauber dynamics is ergodic with probability one and the disorder{averaged of time{autocorrelations decays like e ?m(log t) 2. For the standard dilute Ising ferromagnet with i...
متن کاملGlauber Dynamics for Fermion Point Processes
We construct a Glauber dynamics on {0, 1}, R a discrete space, with infinite range flip rates, for which a fermion point process is reversible. We also discuss the ergodicity of the corresponding Markov process and the log-Sobolev inequality.
متن کامل