A Lyapunov function for Glauber dynamics on lattice triangulations
نویسندگان
چکیده
منابع مشابه
A Lyapunov function for Glauber dynamics on lattice triangulations
We study random triangulations of the integer points [0, n] ∩ Z, where each triangulation σ has probability measure λ|σ| with |σ| denoting the sum of the length of the edges in σ. Such triangulations are called lattice triangulations. We construct a height function on lattice triangulations and prove that, in the whole subcritical regime λ < 1, the function behaves as a Lyapunov function with r...
متن کاملDynamics of Lattice Triangulations on Thin Rectangles
We consider random lattice triangulations of n×k rectangular regions with weight λ|σ| where λ > 0 is a parameter and |σ| denotes the total edge length of the triangulation. When λ ∈ (0, 1) and k is fixed, we prove a tight upper bound of order n for the mixing time of the edge-flip Glauber dynamics. Combined with the previously known lower bound of order exp(Ω(n)) for λ > 1 [3], this establishes...
متن کاملA Note on the Glauber Dynamics for Sampling Independent Sets
This note considers the problem of sampling from the set of weighted independent sets of a graph with maximum degree ∆. For a positive fugacity λ, the weight of an independent set σ is λ|σ|. Luby and Vigoda proved that the Glauber dynamics, which only changes the configuration at a randomly chosen vertex in each step, has mixing time O(n log n) when λ < 2 ∆−2 for triangle-free graphs. We extend...
متن کاملZero temperature Glauber dynamics on complex networks
We study the Glauber dynamics at zero temperature of spins placed on the vertices of an uncorrelated network with a power law degree distribution. Application of mean-field theory yields as the main prediction that for symmetric disordered initial conditions the mean time for reaching full order is finite or diverges as a logarithm of the system size N , depending on the exponent of the degree ...
متن کاملGlauber Dynamics on Trees and Hyperbolic Graphs
We study continuous time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with n vertices and of bounded degree. We Research supported by Microsoft graduate fellowship. Supported by a visiting position at INRIA and a PostDoc at Microsoft research. Research supported by NSF Grants DMS-0104073, CCR-0121555 and a Mill...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2016
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-016-0735-z