Fractional P(phi)(1)-processes and Gibbs measures Kamil Kaleta Jozsef Lorinczi 2134/21396 https://repository.lboro.ac.uk/articles/journal_contribution/Fractional_P_phi_1_-processes_and_Gibbs_measures/9389087 We define and prove existence of fractional P(phi)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. 2016-05-27 13:05:19 Symmetric stable process Fractional Schrodinger operator Intrinsic ultracontractivity Decay of ground state Gibbs measure Statistics Mathematical Sciences not elsewhere classified