Dear all.
The next session of the One World Probability Seminar will be next week on Thursday (November 16) from 14:00 to 16:00 UTC time. The speakers of this session are Elisabetta Candellero (Universita Roma Tre) and Thomas Finn (Durham University).
Title, abstract and the zoom link are below the signature and can be also found on the website https://www.owprobability.org/one-world-probability-seminar.
Kind regards, Ilya Chevyrev and Julio Backhoff.
Title: Coexistence in competing first-passage percolation
Abstract: Consider the following random competition model on a given graph G that is driven by two first-passage percolation processes FPP_1 and FPP_\lambda. Initially, FPP_1 occupies a single site and FPP_\lambda is dormant in seeds that are placed on the sites of G as a product of Bernoulli measures of parameter p. Then, FPP_1 spreads through the edges of G at rate 1 and FPP_\lambda spreads from seeds at rate \lambda when that seed is attempted to be occupied by either FPP_1 or FPP_\lambda. Once a site is occupied by either process it remains occupied by that process henceforth. This model is known as first-passage percolation in a hostile environment (FPPHE) and was first introduced by Sidoravicius and Stauffer ’19.
In the first talk, we establish that FPPHE is non-monotone in the sense that increasing p or \lambda may increase the probability that FPP_1 occupies infinitely many sites through constructing a quasi-transitive graph where such behaviour holds. The non-monotonicity of FPPHE makes understanding the phase transitions of the model extremely challenging. We prove that a regime of coexistence exists on hyperbolic and non-amenable vertex transitive graphs where both FPP_1 and FPP_\lambda concurrently occupy infinite connected components with positive probability.
In the second talk, we prove that a regime of coexistence also holds on Z^d for d>2 through the introduction of a refined multi-scale analysis that can handle non-equilibrium and non-monotone processes. We relate this proof to recent work on multi-particle diffusion limited aggregation by Sidoravicius and Stauffer ’19 and the SIR model by Dauvergne and Sly ’22 where FPPHE is a crucial analytical tool in understanding non-equilibrium particle systems. Based on joint work with Alexandre Stauffer.
Speaker 1 (14:00-15:00 UTC): Elisabetta Candellero (Universita Roma Tre). Speaker 2 (15:00-16:00 UTC): Thomas Finn (Durham University).
Zoom-link: https://univienna.zoom.us/j/69711117344?pwd=Y3cwMEI3VkZKSTh5RVZRSGhRN3lUdz09
Meeting ID: 697 1111 7344 Passcode: 305805