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5 papers · 1 filter
The Potts model built on sand
E. Dinaburg, C. Maes, S. Pirogov +2
We consider the q=4 Potts model on the square lattice with an additional hard-core nonlocal interaction. That interaction arises from the choice of the reference measure taken to b…
Harmonic analysis on the infinite symmetric group
Sergei Kerov, Grigori Olshanski, Anatoly Vershik
Let S be the group of finite permutations of the naturals 1,2,... The subject of the paper is harmonic analysis for the Gelfand pair (G,K), where G stands for the product of two co…
A definable nonstandard model of the reals
Vladimir Kanovei, Saharon Shelah
We prove in ZFC the existence of a definable, countably saturated elementary extension of the reals. It seems that it has been taken for granted that there is no distinguished, def…
Provable first-order transitions for liquid crystal and lattice gauge models with continuous symmetries
A. C. D. van Enter, S. B. Shlosman
We consider various sufficiently nonlinear sigma models for nematic liquid crystal ordering of RP^{N-1} type and of lattice gauge type with continous symmetries. We rigorously show…
Random partitions and the Gamma kernel
Alexei Borodin, Grigori Olshanski
We study the asymptotics of certain measures on partitions (the so-called z-measures and their relatives) in two different regimes: near the diagonal of the corresponding Young dia…