# Davies-Gaffney-Grigor'yan lemma on simplicial complexes

## TL;DR

This paper extends the Davies-Gaffney-Grigor'yan lemma to heat kernels associated with bounded discrete Hodge Laplacians on simplicial complexes, providing new theoretical insights into their properties.

## Contribution

It introduces a novel proof of the Davies-Gaffney-Grigor'yan lemma in the context of simplicial complexes with bounded discrete Hodge Laplacians.

## Key findings

- Established the lemma for heat kernels on simplicial complexes.
- Provided bounds and estimates for heat kernels in this setting.
- Enhanced understanding of spectral properties of discrete Hodge Laplacians.

## Abstract

We prove Davies-Gaffney-Grigor'yan lemma for heat kernels of bounded discrete Hodge Laplacians on simplicial complexes.