We investigate the typical cycle lengths, the total number of cycles, and the number of finite cycles in random permutations whose probability involves cycle weights. Typical cycle lengths and totalâ€¦ (More)

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 anâ€¦ (More)

A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat KoteckÃ½â€“Preiss criterion. Expressions andâ€¦ (More)

We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles growsâ€¦ (More)

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 secondâ€¦ (More)

A powerful tool for the study of self-avoiding walks is the lace expansion of Brydges and Spencer [BS]. It is applicable above four dimensions and shows the mean-field behavior of self-avoidingâ€¦ (More)

In this note we describe some results concerning non-relativistic quantum systems at positive temperature and density confined to macroscopically large regions, Î›, of physical space R which are underâ€¦ (More)

CLUSTER EXPANSION WITH APPLICATIONS 3 In order to guess the correct form of a, one should consider the left side of the equation above with a(y) â‰¡ 0. The integral may depend on x; a typical situationâ€¦ (More)

The Falicov-Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with an on-site repulsion; alternatively, it is a model of itinerant electrons andâ€¦ (More)