[general_dat] Seminario ModEsto - Santiago Saglietti (PUC)

[Sebastian Zaninovich]

*Seminario de Modelos Estocásticos.*

*Viernes 15/5, 12.00hs. Sala de conferencias del Departamento de Matemática*

*Santiago Saglietti *(Pontificia Universidad Católica de Chile)

*A Limit in Law for the Cover Time and Last Visited Vertex of Wired Planar
Domains*

*Resumen:*
We derive a scaling limit in law as N tends to infinity for the cover time
by a simple random walk of the subgraph of the square lattice obtained by
discretizing an N-scale blow up of a planar domain and adding a wired
boundary to it. The limiting distribution is that of a Gumbel random
variable shifted by an independent (random) quantity which is equal to the
full mass of a variant of the critical Liouville Quantum Gravity Measure on
the same domain. We also derive a limit in law for the rescaled location of
the last visited vertex by the walk. Here the limit turns out to be
precisely the (expected) critical Liouville Measure, normalized by its
total mass. Both limits hold jointly with the limiting joint law explicitly
described. These results resolve well-known open problems in the field, in
the case of wired boundary conditions. The proof is based on comparison
with the extremal landscape of the discrete Gaussian Free Field and, in
particular, with that of the discrete Gaussian Free Field conditioned to
have zero average. Joint work with Oren Louidor (Technion).

Están todas/os invitadas/os.

Para más información sobre el grupo de probabilidad:
https://mate.dm.uba.ar/~modesto/

*Los encuentros del seminario ModEsto tienen lugar los viernes a las
12.00hs. Son abiertos a todo público y mayormente informales así que no
siempre los anunciamos por esta vía. Quienes quieran recibir información de
todos los encuentros, por favor unirse al grupo de telegram o enviarme un
mail.

https://t.me/+EHK1RU3WS4YyMzdh