Permanental sequences that are related to a Markov chain example of Kolmogorov

Abstract

Permanental sequences with non-symmetric kernels that are generalization of the potentials of a Markov chain with state space $\{0,1/2,\dots ,1/n,\dots \}$ that was introduced by Kolmogorov, are studied. Depending on a parameter in the kernels we obtain an exact rate of divergence of the sequence at $0$, an exact local modulus of continuity of the sequence at $0$, or a precise bounded discontinuity for the sequence at $0$.