Neumann Heat kernel monotonicity

Abstract

We prove that the diagonal of the transition probabilities for the d-dimensional Bessel processes on (0, 1], reflected at 1, which we denote by $p_R^N(t,r,r)$, is an increasing function of r for d>2 and that this is false for d=2.

Cited by in corpus (10)

• Bordism groups of solutions to differential relations
• Fold cobordisms and a Poincare-Hopf type theorem for the signature
• The bordism version of the h-principle
• Singular cobordism categories
• Invariants of singular sets of smooth maps
• Erratum to "Cobordisms of maps with singularities of given class"
• Universal Lefschetz fibrations and Lefschetz cobordisms
• Computations on cobordism groups of projected immersions
• Fold maps, framed immersions and smooth structures
• The weak b-principle: Mumford conjecture