Domokos Szász (BME MI)
Spectral gap in a stochastic energy model
<br><br>
Abstract: In 2008, Pierre Gaspard and Thomas Gilbert formu-
lated a two step strategy for obtaining the heat equation from
microscopic principles through a Markov jump process of ener-
gies. Their mechanical model was one of localized hard disks
(balls). Here we consider a linear chain of N particles each 
car-
rying an energy. The evolution of the energies is governed by a
continuous time, pure jump Markov process. The interactions are
nearest neighbor ones preserving the energy. (This family of 
sto-
chastic evolutions contains the models of Gaspard and Gilbert.)
A lower bound (in terms of N) is presented for the spectral gap
of the Markov generator under the assumption that the station-
ary distributions are reversible and, moreover, reversible 
states
are also characterized. Our spectral bound is just the 
necessary
one for possibly deriving the heat equation. Joint work with A.
Grigo and K. Khanin.