Spatial random permutations with small cycle weights

Abstract

We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in the space and there is an additional weight that involves the length of permutation jumps. We prove the occurrence of infinite macroscopic cycles above a certain critical density.

25 pages, 1 figure

References in corpus (4)

• Percolation transition in the Bose gas II
• Spatial random permutations and infinite cycles
• Random permutations with cycle weights
• On a model of random cycles

Cited by in corpus (12)

• Random permutations with cycle weights
• Spatial random permutations and Poisson-Dirichlet law of cycle lengths
• Cycle structure of random permutations with cycle weights
• Critical Temperature of Dilute Bose Gases
• Asymptotic statistics of cycles in surrogate-spatial permutations
• Random permutations of a regular lattice
• Macroscopic loops in the Bose gas, Spin O(N) and related models
• Multiplicative arithmetic functions and the generalized Ewens measure
• Scaling limit of a self-avoiding walk interacting with spatial random permutations
• On statistics of permutations chosen from the Ewens distribution
• Coexistence, enhancements and short loops in random walk loop soups
• Short cycles of random permutations with cycle weights: point processes approach