Seminari

Non-equilibrium multi-scale analysis and coexistence in competing first passage percolation

Thomas Finn

12-10-2020 - 14:00
Largo San Leonardo Murialdo,1 - Pal.C - Aula 211

 

We consider a natural random growth process with competition on Z^d called first passage percolation in a hostile environment (FPPHE), in which two processes compete for the occupancy of sites. The first starts at the origin and spreads through the edges of Z^d at rate 1, while the second is initially dormant in seeds, which are distributed as a product of Bernoulli random variables of parameter p on Z^d, and grows from a seed at rate lambda>0 once either process attempts to occupy that seed. Depending on the value of p and lamba, the model observes a rich behaviour with multiple phase transitions. We prove that there is a coexistence phase in which both processes occupy a positive density of sites, which is a stark contrast to the behaviour of other competition models on Z^d.

In studying FPPHE, we introduce a novel approach to multi-scale analysis that can be used to analyse processes with non-equilibrium dynamics. Indeed, FPPHE lacks both equilibrium dynamics and monotonicity (adding a seed could benefit the first process), preventing the use of a more standard multi-scale approach. In this talk, we outline our main results for FPPHE and provide an overview for how this new multi-scale approach can be applied.
Il seminario si svolgera' in modalita' MISTA:

IN PRESENZA: presso l'aula 211, palazzina C di Largo San Leonardo
Murialdo 1. La capienza massima dell'aula e' di circa 10 persone;
preghiamo chi intenda partecipare in presenza di scrivere un messaggio

astauffer@mat.uniroma3.it

DA REMOTO:  Per partecipare al seminario cliccare sul seguente link

https://teams.microsoft.com/l/meetup-join/19%3ameeting_OTk4MzI5MzktY2EzNS00NjFkLTg1N2ItYjFiZTNiY2Q3NTUy%40thread.v2/0?context=%7b%22Tid%22%3a%22ffb4df68-f464-458c-a546-00fb3af66f6a%22%2c%22Oid%22%3a%22e29bc6f2-5252-4a64-ac1d-48181052aeb7%22%7d
org: STAUFFER Alexandre

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