The intersection of combinatorics and statistical physics has experienced great activity in recent years. This flurry of activity has been fertilized by an exchange not only of techniques, but also of objectives. Computer scientists interested in approximation algorithms have helped statistical physicists and discrete mathematicians overcome language problems. They have found a wealth of common ground in probabilistic combinatorics. Close connections between percolation and random graphs, graph morphisms and hard-constraint models, and slow mixing and phase transition have led to new results and perspectives. These connections can help in understanding typical behavior of combinatorial phenomena such as graph coloring and homomorphisms. Inspired by issues and intriguing new questions surrounding the interplay of combinatorics and statistical physics, a DIMACS/DIMATIA workshop was held at Rutgers University. These proceedings are the outgrowth of that meeting. This volume is intended for graduate students and research mathematicians interested in probabilistic graph theory and its applications.
Efficient local search near phase transitions in combinatorial optimization by S. Boettcher On the sampling problem for $H$-colorings on the hypercubic lattice by C. Borgs, J. T. Chayes, M. Dyer, and P. Tetali Graph homomorphisms and long range action by G. R. Brightwell and P. Winkler Random walks and graph homomorphisms by A. Daneshgar and H. Hajiabolhassan Recent results on parameterized $H$-colorings by J. Diaz, M. Serna, and D. M. Thilikos Rapidly mixing Markov chains for dismantleable constraint graphs by M. Dyer, M. Jerrum, and E. Vigoda On weighted graph homomorphisms by D. Galvin and P. Tetali Counting list homomorphisms for graphs with bounded degrees by P. Hell and J. Nesetril On the satisfiability of random $k$-hom formulae by G. Istrate The exchange interaction, spin hamiltonians, and the symmetric group by J. Katriel A discrete non-Pfaffian approach to the Ising problem by M. Loebl Survey: Information flow on trees by E. Mossel Chromatic numbers of products of tournaments: Fractional aspects of Hedetniemi's conjecture by C. Tardif Perfect graphs for generalized colouring-circular perfect graphs by X. Zhu.