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Short-Time Gibbsianness for Infinite-Dimensional Diffusions with Space-Time Interaction

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Abstract

We consider a class of infinite-dimensional diffusions where the interaction between the components has a finite extent both in space and time. We start the system from a Gibbs measure with a finite-range uniformly bounded interaction. Under suitable conditions on the drift, we prove that there exists t 0>0 such that the distribution at time tt 0 is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion of both the initial interaction and certain time-reversed Girsanov factors coming from the dynamics.

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Correspondence to Frank Redig.

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S. Roelly is on leave of absence Centre de Mathématiques Appliquées, UMR C.N.R.S. 7641, École Polytechnique, 91128 Palaiseau Cédex, France.

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Redig, F., Rœlly, S. & Ruszel, W. Short-Time Gibbsianness for Infinite-Dimensional Diffusions with Space-Time Interaction. J Stat Phys 138, 1124–1144 (2010). https://doi.org/10.1007/s10955-010-9926-7

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  • DOI: https://doi.org/10.1007/s10955-010-9926-7

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