We consider a Markovian growth process on locally finite partially ordered sets \Lambda, equivalent to last passage percolation (LPP) with independent (not necessarily identical) exponentially distributed weights on the elements of \Lambda. Such a process includes inhomogeneous exponential LPP on the Euclidean lattice N^d.
In this talk, we discuss non-asymptotic bounds on the mean and variance of the passage time \tau_A to grow any set A \subset \Lambda in terms of characteristics of A. We also discuss a limit shape theorem when \Lambda is equipped with a `monoid' structure. Methods involve making use of the backward equation associated to the Markovian evolution and comparison inequalities with respect to the time-reversed generator. Based on work with Tanner Resse https://arxiv.org/abs/2602.02856
Zoom link: https://us02web.zoom.us/j/88670406480
Meeting ID: 886 7040 6480