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arXiv · 1011.2713

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

Kamil Kaleta·Jozsef Lorinczi
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Abstract

We define and prove existence of fractional $P(ϕ)_1$-processes as random processes generated by fractional Schrödinger 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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BibTeXRIS

Kamil Kaleta, Jozsef Lorinczi. 2011-09-13. Fractional $P(ϕ)_1$-processes and Gibbs measures. https://doi.org/10.1016/j.spa.2012.06.001

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