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math.CO2022★ 3 cited
Random partitions under the Plancherel-Hurwitz measure, high genus Hurwitz numbers and maps
Guillaume Chapuy, Baptiste Louf, Harriet Walsh
We study the asymptotic behaviour of random integer partitions under a new probability law that we introduce, the Plancherel-Hurwitz measure. This distribution, which has a natural…
math.PR2022★ 3 cited
The Discrete Gaussian model, I. Renormalisation group flow at high temperature
Roland Bauerschmidt, Jiwoon Park, Pierre-François Rodriguez
The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions, at sufficiently high temperature, we show that its macroscopic s…