Seminario - The asymptotic determinant of the discrete Laplacian in non-rectilinear and non-simply-connected polygons

Giovedì 8 ottobre 2020 alle ore 14:30, il prof. Rafael Greenblatt dell’Università degli Studi Roma Tre, terrà il seminario di Fisica Matematica dal titolo: " The asymptotic determinant of the discrete Laplacian in non-rectilinear and non-simply-connected polygons".

Abstract
Consider the discrete Laplacian Delta with Dirichlet boundary conditions on
a domain of the form L Pi, for Pi  a bounded region whose boundary is a
disjoint union of polygons with vertices in Z^2.  I will show that for
large L

- log det Delta = a_0(Pi) L^2 + a_1(Pi) L + a_2(Pi) log L + a_3(Pi) + o(1),

generalizing a previous result by Kenyon (2000).  An expansion of the same
form holds for the modified Laplacians appearing in the partition functions
of dimer models on the associated Temperleyan polyominoes in the
non-simply-connected case, with a_3 changed.

The method of the proof is new, and is based on analyzing an expression for
the determinant in terms of the return probabilities of the continuous time
random walk generated by Delta.  This has the additional feature of
relating a_2 and a_3 to the zeta-regularized determinant of the continuum
Laplacian on Pi via convergence of the aforementioned random walk to a
Brownian motion.

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 a Link identifier #identifier__26300-1giuliani@mat.uniroma3.it.
  • DA REMOTO:  Per partecipare al seminario cliccare sul seguente link Link identifier #identifier__127291-2Teams meeting.
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