A wide class of "counting" problems have been studied in Computer Science. Three typical examples are the estimation of (i) the permanent of an n x n 0-1 matrix, (ii) the partition function of certain n— particle Statistical Mechanics systems and (iii) the volume of an n— dimensional convex set. These problems can be reduced to sampling from the steady state distribution of implicitly defined M...

We prove comparison results for the Swendsen-Wang (SW) dynamics, the heat-bath (HB) dynamics for the Potts model and the single-bond (SB) dynamics for the randomcluster model on arbitrary graphs. In particular, we prove that rapid mixing of HB implies rapid mixing of SW on graphs with bounded maximum degree and that rapid mixing of SW and rapid mixing of SB are equivalent. Additionally, the spe...

CP asymmetry in B → φKS decay is studied in the special context of supersymmetry theories, in which the charginos play an important role. We find that in addition to the gluino, the chargino can also make large contributions to CP asymmetry in B → φKS decay. After considering the constraints from B → J/ψKS decay, we study three special scenarios: (a). Large mixing between left-handed charm and ...

We analyze the possibility of probing the supersymmetric flavor structure through the constraints of the K and B meson systems and those of the electric dipole moments. We show that combining these constraints would favor SUSY models with large flavor mixing either in LR(RL) or LL but with a very small RR and intermediate/large tan β. Large LR mixing requires specific patterns for trilinear A-t...

CP asymmetry in B → φKS decay is studied in a special context of supersymmetry theories, in which the charginos play an important role. We find that except gluino, chargino can also give large contributions to CP asymmetry in B → φKS decay. After considering the constraints from B → J/ψKS decay, we study three special scenarios: (a). Large mixing on left-handed charm and top squarks(LL mixing);...

The eigenvalue or spectral gap of a Markov chain is the difference between the two largest eigenvalues of the transition matrix of its underlying (state space) graph. In this paper we explore the intimate relationship between the spectral gap of a Markov chain and its mixing time, as well as another closely related structural property of a Markov chain known as conductance. The relationships am...

Motivated by the ‘subgraphs world’ view of the ferromagnetic Ising model, we analyse the mixing times of Glauber dynamics based on subset expansion expressions for classes of graph, hypergraph and matroid polynomials. With a canonical paths argument, we demonstrate that the chains defined within this framework mix rapidly upon graphs, hypergraphs and matroids of bounded tree-width. This extends...