Zobrazeno 1 - 8
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pro vyhledávání: '"Alexander Glazman"'
Autor:
Alexander Glazman, Ioan Manolescu
We prove that all Gibbs measures of the $q$-state Potts model on $\mathbb{Z}^2$ are linear combinations of the extremal measures obtained as thermodynamic limits under free or monochromatic boundary conditions. In particular all Gibbs measures are in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5bdbd9a4aeb14b27232087db0246ea4d
Autor:
Alexander Glazman, Ioan Manolescu
Publikováno v:
Progress in Probability ISBN: 9783030607531
We show that the loop O(n) model on the hexagonal lattice exhibits exponential decay of loop sizes whenever n > 1 and \(x 0.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8f23647888a29d381562a1304fd98cd8
https://doi.org/10.1007/978-3-030-60754-8_21
https://doi.org/10.1007/978-3-030-60754-8_21
Autor:
Ioan Manolescu, Alexander Glazman
Publikováno v:
Ann. Inst. H. Poincaré Probab. Statist. 56, no. 4 (2020), 2281-2300
We consider a self-avoiding walk model (SAW) on the faces of the square lattice $\mathbb{Z}^2$. This walk can traverse the same face twice, but crosses any edge at most once. The weight of a walk is a product of local weights: each square visited by
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::27a7723db227b2b2898286d8431b826c
https://projecteuclid.org/euclid.aihp/1603267219
https://projecteuclid.org/euclid.aihp/1603267219
Autor:
Alexander Glazman, Ioan Manolescu
Publikováno v:
Communications in Mathematical Physics
Uniform integer-valued Lipschitz functions on a domain of size $N$ of the triangular lattice are shown to have variations of order $\sqrt{\log N}$. The level lines of such functions form a loop $O(2)$ model on the edges of the hexagonal lattice with
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::99d10ab2e2628cad00d824d2ec325fb2
http://arxiv.org/abs/1810.05592
http://arxiv.org/abs/1810.05592
Publikováno v:
Journal of the European Mathematical Society
The loop $O(n)$ model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin $O(n)$ model. It has been predicted by Nienhuis that for $0\le n\le 2$ the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c4aa0515a8d3263c6df5bbafca00de7c
http://arxiv.org/abs/1707.09335
http://arxiv.org/abs/1707.09335
Publikováno v:
Journal of Mathematical Sciences. 188:591-595
Let F be a nonformally real field, n, r be positive integers. Suppose that for any prime number p ≤ n, the quotient group F */F *p is finite. We prove that if N is large enough, then any system of r forms of degree in N variables over F has a nonze
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b9c6119ab4addf1cd83b1989a411110d
https://doi.org/10.1007/s10958-013-1150-y
https://doi.org/10.1007/s10958-013-1150-y
Publikováno v:
Ann. Probab. 44, no. 2 (2016), 955-983
We prove two results on the delocalization of the endpoint of a uniform self-avoiding walk on Z^d for d>1. We show that the probability that a walk of length n ends at a point x tends to 0 as n tends to infinity, uniformly in x. Also, for any fixed x
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::65dd44c5c910a1e06a065a38fde6f74e
https://doi.org/10.1214/14-aop993
https://doi.org/10.1214/14-aop993
Autor:
Alexander Glazman
Publikováno v:
Electron. Commun. Probab.
We consider a self-avoiding walk on the dual $\mathbb{Z}^2$ lattice. This walk can traverse the same square twice but cannot cross the same edge more than once. The weight of each square visited by the walk depends on the way the walk passes through
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b5d46821a30ccc94a875b6d733caa546
https://doi.org/10.1214/ecp.v20-3844
https://doi.org/10.1214/ecp.v20-3844