Stability of Gibbs distributions

1985 ◽  
Vol 65 (2) ◽  
pp. 1172-1176
Author(s):  
V. V. Krivolapova ◽  
G. I. Nazin
Keyword(s):  
Gibbs Distributions

scholarly journals Coagulation Processes with Gibbsian Time Evolution

2012 ◽  
Vol 49 (03) ◽  
pp. 612-626
Author(s):  
Boris L. Granovsky ◽  
Alexander V. Kryvoshaev
Keyword(s):  
Stochastic Process ◽  
Recurrence Relation ◽  
Time Evolution ◽  
Nonnegative Function ◽  
Gibbs Distribution ◽  
Time Dependent ◽  
Explicit Solutions ◽  
Gibbs Distributions ◽  
Giant Cluster ◽  
Positive Integers

We prove that a stochastic process of pure coagulation has at any timet≥ 0 a time-dependent Gibbs distribution if and only if the rates ψ(i,j) of single coagulations are of the form ψ(i;j) =if(j) +jf(i), wherefis an arbitrary nonnegative function on the set of positive integers. We also obtain a recurrence relation for weights of these Gibbs distributions that allow us to derive the general form of the solution and the explicit solutions in three particular cases of the functionf. For the three corresponding models, we study the probability of coagulation into one giant cluster by timet> 0.

scholarly journals How Gibbs distributions may naturally arise from synaptic adaptation mechanisms

2009 ◽  
Vol 10 (S1) ◽  
Author(s):  
Juan C Vasquez ◽  
Bruno Cessac ◽  
Horacio Rostro-Gonzalez ◽  
Thierry Vieville
Keyword(s):  
Adaptation Mechanisms ◽  
Gibbs Distributions

scholarly journals Gibbs versus non-Gibbs distributions in money dynamics

2004 ◽  
Vol 340 (1-3) ◽  
pp. 334-339 ◽  
Author(s):  
Marco Patriarca ◽  
Anirban Chakraborti ◽  
Kimmo Kaski
Keyword(s):  
Gibbs Distributions

scholarly journals Complexity Analysis of a Sampling-Based Interior Point Method for Convex Optimization

2021 ◽  
Author(s):  
Riley Badenbroek ◽  
Etienne de Klerk
Keyword(s):  
Convex Body ◽  
Interior Point ◽  
Interior Point Method ◽  
Complexity Analysis ◽  
Point Method ◽  
Mixing Times ◽  
Approximation Quality ◽  
Gibbs Distributions ◽  
Hit And Run ◽  
The Mean

We develop a short-step interior point method to optimize a linear function over a convex body assuming that one only knows a membership oracle for this body. The approach is based a sketch of a universal interior point method using the so-called entropic barrier. It is well known that the gradient and Hessian of the entropic barrier can be approximated by sampling from Boltzmann-Gibbs distributions and the entropic barrier was shown to be self-concordant. The analysis of our algorithm uses properties of the entropic barrier, mixing times for hit-and-run random walks, approximation quality guarantees for the mean and covariance of a log-concave distribution, and results on inexact Newton-type methods.

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