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DTSTART:20210328T030000
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DTSTAMP:20210922T061631Z
UID:1610469000@ist.ac.at
DTSTART:20210112T173000
DTEND:20210112T181500
DESCRIPTION:Speaker: Marcin Lis\nhosted by M. Beiglböck\, N. Berestycki\,
L. Erdös\, J. Maas\, F. Toninelli\nAbstract: The classical dimer model is
a uniform probability measure on the space of perfect matchings of a grap
h\, i.e.\, sets of edges such that each vertex is incident on exactly one
edge. In two dimensions\, one can define an associated height function whi
ch naturally models a ''uniform'' random surface (with specified boundary
conditions). Moreover the model can be solved exactly which in particular
means that its correlations are given by the entries of the inverse Kaste
leyn matrix. This exact solvability was the starting point for the breakth
rough work of Kenyon who proved\, already 20 years ago\, that the scaling
limit of the height function in bounded domains approximated by the squar
e lattice with vanishing mesh is the Dirichlet (or zero boundary condition
s) Gaussian free field. This was the first mathematically rigorous example
of conformal invariance in planar statistical mechanics. In this talk\, I
will focus on a natural modification of the model where one allows the ve
rtices on the boundary of the graph to remain unmatched. This is the so-c
alled monomer-dimer model (or dimer model with free boundary conditions) (
in our case the presence of monomers is restricted to the boundary). This
modification complicates the classical analysis in several ways and I will
discuss how to circumvent the arising obstacles. In the end\, the main re
sult that we obtain is that the scaling limit of the height function of th
e monomer-dimer model in the upper half-plane approximated by the square l
attice with vanishing mesh is the Neumann (or free boundary conditions) Ga
ussian free field.This is based on joint work with Nathanael Berestycki (V
ienna) and Wei Qian (Paris).
LOCATION:online via Zoom\, IST Austria
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Marcin Lis: The monomer-dimer model and the Neumann Gaussian Free f
ield
URL:https://talks-calendar.app.ist.ac.at/events/3025
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