Research output: Contribution to journal › Article › peer-review
Original language | English |
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Pages (from-to) | 543-587 |
Number of pages | 45 |
Journal | PROBABILITY THEORY AND RELATED FIELDS |
Volume | 179 |
Issue number | 3-4 |
DOIs | |
Accepted/In press | 30 Nov 2020 |
Published | 7 Feb 2021 |
Additional links |
We study a random permutation of a lattice box in which each permutation is given a Boltzmann weight with energy equal to the total Euclidean displacement. Our main result establishes the band structure of the model as the box-size N tends to infinity and the inverse temperature β tends to zero; in particular, we show that the mean displacement is of order min { 1 / β, N}. In one dimension our results are more precise, specifying leading-order constants and giving bounds on the rates of convergence. Our proofs exploit a connection, via matrix permanents, between random permutations and Gaussian fields; although this connection is well-known in other settings, to the best of our knowledge its application to the study of random permutations is novel. As a byproduct of our analysis, we also provide asymptotics for the permanents of Kac–Murdock–Szegő matrices.
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