[ABE-L] Próximo seminário (online) de probabilidade - 1 de março

[Maria Eulalia Vares]

*Probability Webinar -   IM-UFRJ *



Dear colleagues,

Our next online seminar will be held on Monday, *March 1st*, from *3 p.m.
to 4 p.m*. (Rio de Janeiro local time)

The GoogleMeet link for the seminar is  https://meet.google.com/uew-ehhn-kby




Speaker:   *Ines Armendariz  (UBA) *

Title: *Gaussian random permutations and the boson point process *

Abstract: We construct an infinite volume spatial random permutation
associated to a Gaussian Hamiltonian, which is parametrized by the point
density and the temperature. Spatial random permutations are naturally
related to boson systems through a representation originally due to Feynman
(1953). Bose-Einstein condensation occurs for dimensions 3 or larger, above
a critical density, and is manifest in this representation by the presence
of cycles of macroscopic length. For subcritical densities we define the
spatial random permutation as a Poisson process of finite unrooted loops of
a random walk with Gaussian increments that we call Gaussian loop soup,
analogous to the Brownian loop soup of Lawler and Werner (2004). We also
construct Gaussian random interlacements, a Poisson process of
doubly-infinite trajectories of random walks with Gaussian increments
analogous to the Brownian random interlacements of Sznitman (2010). For
dimensions greater than or equal to 3 and supercritical densities, we
define the spatial permutation as the superposition of independent
realizations of the Gaussian loop soup at critical density and Gaussian
random interlacements at the remaining density. We show some properties of
these spatial permutations, in particular that the point marginal is the
boson point process, for any point density.

This is joint work with P.A. Ferrari and S. Yuhjtman.



All the talks are held in English.

The videos of the online seminars held in 2020 are available at
http://www.dme.ufrj.br/?page_id=2885

For the 2021 series, a few days after each meeting the video should be
available at http://www.dme.ufrj.br/?page_id=3027



Thanks for circulating this information.

Sincerely,
Organizers: Guilherme Ost and Maria Eulalia Vares
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