Fractional $P(φ)_1$-processes and Gibbs measures

Details Fractional $P(φ)_1$-processes and Gibbs measures Fractional $P(φ)_1$-processes and Gibbs measures

2010-11-11

arxiv.org/abs/1011.2713v2

Mathematics

Probability

37 pages

Scientific paper

We define and prove existence of fractional $P(\phi)_1$-processes as random processes generated by fractional Schr\"odinger semigroups with Kato-decomposable potentials. Also, we show that the measure of such a process is a Gibbs measure with respect to the same potential. We give conditions of its uniqueness and characterize its support relating this with intrinsic ultracontractivity properties of the semigroup and the fall-off of the ground state. To achieve that we establish and analyze these properties first.

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