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The East process, a well known reversible linear chain of spins, represents the prototype of a general class of interacting particle systems with constraints modeling the dynamics of real glasses. In this paper we consider a generalization of the East process living in the d-dimensional lattice and we establish new progresses on the out- of-equilibrium behavior. In particular we prove a form of (local) exponential ergodicity when the initial distribution is far from the stationary one and we prove that the mixing time in a finite box grows linearly in the side of the box

annales de la faculté des sciences de toulouse/annales de la faculté des sciences de toulouse

Mixing time and local exponential ergodicity of the East-like process in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>ℤ</mml:mi> <mml:mi>d</mml:mi> </mml:msup></mml:math>

Mixing time and local exponential ergodicity of the East-like process in ℤ d