Related papers: The Mixing Time of Glauber Dynamics for Colouring …

We study the ferromagnetic random field Ising model (RFIM) on a graph $G=(V,E)$ having maximal degree $\Delta$, where the external field at each vertex is an i.i.d. random variable. When the random field distribution is sufficiently…

We prove an upper bound on the total variation mixing time of a finite Markov chain in terms of the absolute spectral gap and the number of elements in the state space. Unlike results requiring reversibility or irreducibility, this bound is…

We investigate the Glauber dynamics of the generalized (2+1)-dimensional $p$-SOS model under a hard floor constraint. This setting induces entropic repulsion: the integer-valued interface height is forced to remain above the wall and…

Let $G = (V,E)$ be a graph on $n$ vertices and let $m^*(G)$ denote the size of a maximum matching in $G$. We show that for any $\delta > 0$ and for any $1 \leq k \leq (1-\delta)m^*(G)$, the down-up walk on matchings of size $k$ in $G$ mixes…

We consider the problem of maintaining a $(1+\epsilon)\Delta$-edge coloring in a dynamic graph $G$ with $n$ nodes and maximum degree at most $\Delta$. The state-of-the-art update time is $O_\epsilon(\text{polylog}(n))$, by Duan, He and…

We study the Glauber dynamics for heavy-tailed spin glasses, in which the couplings are in the domain of attraction of an $\alpha$-stable law for $\alpha\in (0,1)$. We show a sharp description of metastability on exponential timescales, in…

We characterize the extremal structure for the exact mixing time for random walks on trees $T_{n,d}$ of order $n$ with diameter $d$. Given a graph $G=(V,E)$, let $H(v,\pi)$ denote the expected length of an optimal stopping rule from vertex…

In a bounded max-coloring of a vertex/edge weighted graph, each color class is of cardinality at most $b$ and of weight equal to the weight of the heaviest vertex/edge in this class. The bounded max-vertex/edge-coloring problems ask for…

The mixing time of a random walk, with or without backtracking, on a random graph generated according to the configuration model on $n$ vertices, is known to be of order $\log n$. In this paper we investigate what happens when the random…

We call a proper edge coloring of a graph $G$ a B-coloring if every 4-cycle of $G$ is colored with four different colors. Let $q_B(G)$ denote the smallest number of colors needed for a B-coloring of $G$. Motivated by earlier papers on…

We give a survey of the known results on mixing time of Glauber dynamics for the Ising model on the square lattice and present a technique that makes exact sampling of the Ising model at all temperatures possible in polynomial time. At high…

We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature $\beta$ and random boundary conditions $\tau$ whose distribution P either stochastically dominates the extremal plus phase (hence the…

We study the sampling problem for simultaneous edge colorings. Given a pair of graphs $G_1=(V,E_1)$ and $G_2=(V,E_2)$ which are on the same vertex set $V$, a simultaneous edge coloring is an edge coloring of $G_1\cup G_2$ so that each of…

Conventional wisdom in the sampling literature, backed by a popular diffusion scaling limit, suggests that the mixing time of the Metropolis-Adjusted Langevin Algorithm (MALA) scales as $O(d^{1/3})$, where $d$ is the dimension. However, the…

Let $G$ be a graph on $n$ vertices of maximum degree $\Delta$. We show that, for any $\delta > 0$, the down-up walk on independent sets of size $k \leq (1-\delta)\alpha_c(\Delta)n$ mixes in time $O_{\Delta,\delta}(k\log{n})$, thereby…

We consider congestion dynamics with $n$ players and $Q$ resources under the constraint that the number of each resource is $\kappa$ and that $n<\kappa Q$ in the regime that $n$ and $\kappa$ diverge but $Q$ is fixed with $n=\lfloor{\rho…

Consider $k$-colorings of the complete tree of depth $\ell$ and branching factor $\Delta$. If we fix the coloring of the leaves, as $\ell$ tends to $\infty$, for what range of $k$ is the root uniformly distributed over all $k$ colors? This…

We develop a new technique for proving cell-probe lower bounds on dynamic data structures. This technique enables us to prove an amortized randomized Omega(lg n) lower bound per operation for several data structural problems on n elements,…

In this paper we study metastable behaviour at low temperature of Glauber spin-flip dynamics on random graphs. We fix a large number of vertices and randomly allocate edges according to the Configuration Model with a prescribed degree…

We analyze the vertex Zff in the framework of models that add a new bottom quark in a nonsequential way and we evaluate the tree level contribution to LEP/SLC data $R_{b}$, $R_{l}$ and the total Z width $\Gamma_{Z}$. We obtain bounds for…