Strong spatial mixing of list coloring of graphs
The property of spatial mixing and strong spatial mixing in spin systems has been of interest because of its implications on uniqueness of Gibbs measures on infinite graphs and efficient approximation of counting problems that are otherwise known to be #...
A generalized Pólya's urn with graph based interactions
Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability proportional ...
Cycle length distributions in random permutations with diverging cycle weights
We study the model of random permutations with diverging cycle weights, which was recently considered by Ercolani and Ueltschi, and others. Assuming only regular variation of the cycle weights we obtain a very precise local limit theorem for the size of ...
A note on the quicksort asymptotics
In a recent paper, Bindjeme and Fill obtained a surprisingly easy exact formula for the L2-distance of the normalized number of comparisons of Quicksort under the uniform model to its limit. Shortly afterwards, Neininger proved a central limit theorem ...
Limit distribution of the coefficients of polynomials with only unit roots
We consider sequences of random variables whose probability generating functions have only roots on the unit circle, which has only been sporadically studied in the literature. We show that the random variables are asymptotically normally distributed if ...
The poset of hypergraph quasirandomness
Chung and Graham began the systematic study of k-uniform hypergraph quasirandom properties soon after the foundational results of Thomason and Chung-Graham-Wilson on quasirandom graphs. One feature that became apparent in the early work on k-uniform ...
