Thesis

We look at geometric limits of large random non-uniform permutations. We mainly consider two theories for limits of permutations: permuton limits, introduced by Hoppen, Kohayakawa, Moreira, Rath, and Sampaio to define a notion of scaling limits for permutations; and Benjamini-Schramm limits, introduced by the author to define a notion of local limits for permutations. The models of …

[Ph.D] Random Permutations: A geometric point of viewRead More »

Existence of phase transition for the level-set percolation for the discrete Gaussian free field on  (DGFF) is a problem that received much attention in the past years, in particular it was studied in the 80’s by J. Bricmont, J.L. Lebowitz and C. Maes. They showed that in three dimension the DGFF has a nontrivial percolation …

[M.Sc] Level-set percolation for the Gaussian free fieldRead More »