Spatial random permutations and infinite cycles

Abstract

We consider systems of spatial random permutations, where permutations are weighed according to the point locations. Infinite cycles are present at high densities. The critical density is given by an exact expression. We discuss the relation between the model of spatial permutations and the ideal and interacting quantum Bose gas.

31 pages

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Cited by in corpus (27)

• Random permutations with cycle weights
• Spatial random permutations and Poisson-Dirichlet law of cycle lengths
• Spatial random permutations with small cycle weights
• Cycle structure of random permutations with cycle weights
• Lattice permutations and Poisson-Dirichlet distribution of cycle lengths
• A variational formula for the free energy of an interacting many-particle system
• Critical Temperature of Dilute Bose Gases
• Regenerative random permutations of integers
• On the number of cycles in a random permutation
• Infinite cycles in the random stirring model on trees
• Asymptotic statistics of cycles in surrogate-spatial permutations
• Random permutations of a regular lattice
• Random partitions in statistical mechanics
• Macroscopic loops in the Bose gas, Spin O(N) and related models
• Formation of infinite loops for an interacting bosonic loop soup
• Gibbs measures on permutations over one-dimensional discrete point sets
• A new approach to the characteristic polynomial of a random unitary matrix
• Shift in critical temperature for random spatial permutations with cycle weights
• Emergence of interlacements from the finite volume Bose soup
• Finite cycle Gibbs measures on permutations of ${\mathbb{Z}}^d$
• The model of interacting spatial permutations and its relation to the Bose gas
• Multiplicative arithmetic functions and the generalized Ewens measure
• Coexistence, enhancements and short loops in random walk loop soups
• Off-diagonal long-range order for the free Bose gas via the Feynman--Kac formula
• Infinite cycles of interacting bosons
• Simultaneous occurrence of off-diagonal long-range order and infinite permutation cycles in systems of interacting atoms
• Correlation for permutations