[ABE-L] Probability Webinar - IM-UFRJ - 14/09

[Maria Eulalia Vares]

*Probability Webinar -   IM-UFRJ *



Dear colleagues,

Our next online seminar will be held on Monday, September 14, from *3 p.m.
to 4 p.m*. (Rio de Janeiro local time)

The GoogleMeet link for the seminars is:
https://meet.google.com/nxh-optr-wtq

Speaker:  *Alexandre Stauffer*  (Università Roma Tre and University of Bath)

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

Abstract:  We consider a natural random growth process with competition on
Z^d called first-passage percolation in a hostile environment, that
consists of two first-passage percolation processes FPP_1 and FPP_\lambda
that compete for the occupancy of sites. Initially FPP_1 occupies the
origin and spreads through the edges of Z^d at rate 1, while FPP_\lambda is
initialised at sites called seeds that are distributed according to a
product of Bernoulli measures of parameter p. A seed remains dormant until
FPP_1 or FPP_\lambda attempts to occupy it, after which it spreads through
the edges of Z^d at rate \lambda. We will discuss the results known for
this model and present a recent proof that the two types can coexist
(concurrently produce an infinite cluster) on Z^d. We remark that, though
counterintuitive, the above model is not monotone in the sense that adding
a seed of FPP_\lambda could favor FPP_1.
A central contribution of our work is the development of a novel
multi-scale analysis to analyze this model, which we call a multi-scale
analysis with non-equilibrium feedback and which we believe could help
analyze other models  with non-equilibrium dynamics and lack of
monotonicity. A crucial step in our analysis is the addition of some
non-local events  to the multi-scale framework, and interplaying the
non-local events with a by now "standard" multi-scale renormalization.

Based on a joint work with Tom Finn (Univ. of Bath).



All the talks are held in English.

Thanks for circulating this information.

Sincerely,
Organizers: Guilherme Ost and Maria Eulalia Vares
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