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math.PR2026
Heat kernel estimates on book-like graphs
Emily Dautenhahn, Laurent Saloff-Coste
In this paper, we prove two-sided heat kernel estimates on what we call "book-like" graphs. These are graphs consisting of pieces that satisfy the parabolic Harnack inequality that…
math.PR2026
Faber-Krahn inequality and heat kernel estimates on glued graphs
Emily Dautenhahn, Laurent Saloff-Coste
Faber-Krahn functions provide lower bounds on the first Dirichlet eigenvalue of the Laplacian and are useful because they imply heat kernel upper bounds. In this paper, we are inte…
math.PR2025
Hitting probabilities and uniformly -transient subgraphs
Emily Dautenhahn, Laurent Saloff-Coste
We study the probability that a random walk started inside a subgraph of a larger graph exits that subgraph (or, equivalently, hits the exterior boundary of the subgraph). Consider…