Annealed Pucci Estimate For Markov Chains on Z^d

COLLOQUIUM TALK

Abstract: We discuss the ABP estimate and why it has been challenging to obtain it in the nonlocal setup. We then present a discrete version of the estimate which holds for Markov chains with large jumps. The jumps can have polynomially decaying tails although our result is new even when the decay is exponential. Our proof relies on the construction of 'random' barriers to a discrete Monge–Ampère operator. The talk is based on ongoing work with Moritz Kaßmann.

Speaker Bio: Harsh Prasad is a postdoc at the Fakultät für Mathematik, Universität Bielefeld, Germany. He completed his Ph.D. in Mathematics at the TIFR  Centre for Applicable Mathematics, Bengaluru, in 2024. His research interests include regularity theory and numerical analysis for nonlocal pde and their application to peridynamics. He is also interested in discrete/probabilistic methods in regularity theory.

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