Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On non-local ergodic Jacobi semigroups: spectral theory,
  convergence-to-equilibrium and contractivity   In this paper, we introduce and study non-local Jacobi operators, which
generalize the classical (local) Jacobi operators. We show that these operators
extend to generators of ergodic Markov semigroups with unique invariant
probability measures and study their spectral and convergence properties. In
particular, we derive a series expansion of the semigroup in terms of
explicitly defined polynomials, which generalize the classical Jacobi
orthogonal polynomials. In addition, we give a complete characterization of the
spectrum of the non-self-adjoint generator and semigroup. We show that the
variance decay of the semigroup is hypocoercive with explicit constants, which
provides a natural generalization of the spectral gap estimate. After a random
warm-up time, the semigroup also decays exponentially in entropy and is both
hypercontractive and ultracontractive. Our proofs hinge on the development of
commutation identities, known as intertwining relations, between local and
non-local Jacobi operators and semigroups, with the local objects serving as
reference points for transferring properties from the local to the non-local
case.

19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas