English

Uniform approximation of the heat kernel on a manifold

Probability 2020-03-03 v4 Differential Geometry

Abstract

We approximate the heat kernel h(x,y,t)h(x,y,t) on a compact connected Riemannian manifold MM without boundary uniformly in (x,y,t)M×M×[a,b](x,y,t)\in M\times M\times [a,b], a>0a>0, by nn-fold integrals over MnM^n of the densities of Brownian bridges. Moreover, we provide an estimate for the uniform convergence rate. As an immediate corollary, we get a uniform approximation of solutions of the Cauchy problem for the heat equation on MM.

Keywords

Cite

@article{arxiv.math/0701281,
  title  = {Uniform approximation of the heat kernel on a manifold},
  author = {Evelina Shamarova and Alexandre B. Simas},
  journal= {arXiv preprint arXiv:math/0701281},
  year   = {2020}
}

Comments

Minor corrections

R2 v1 2026-07-22T17:49:09.069Z