Investigation of Conditions for the Asymptotic Existence of the Configuration Integral of Gibbs’ Distribution

1964 ◽  
Vol 9 (4) ◽  
pp. 566-581 ◽  
Author(s):  
R. L. Dobrushin
Keyword(s):  
Gibbs Distribution ◽  
Configuration Integral

A proposal to determine the configuration integral of non-ideal gas

1994 ◽  
Vol 16 (5) ◽  
pp. 449-452
Author(s):  
Wang Jianmin ◽  
Xu Shushan
Keyword(s):  
Ideal Gas ◽  
Configuration Integral

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.

Application of the Gibbs distribution to image segmentation

2005 ◽  
Author(s):  
H. Elliott ◽  
H. Derin ◽  
R. Cristi ◽  
D. Geman
Keyword(s):  
Image Segmentation ◽  
Gibbs Distribution

scholarly journals Income distribution in the Colombian economy from an econophysics perspective

2016 ◽  
Vol 35 (69) ◽  
pp. 691-707
Author(s):  
Hernando Quevedo Cubillos ◽  
María N. Quevedo
Keyword(s):  
Income Distribution ◽  
Economic System ◽  
Power Law ◽  
Gibbs Distribution ◽  
Economic Systems ◽  
Second Phase ◽  
Equilibrium Thermodynamic ◽  
Thermodynamic Models ◽  
Density Distributions ◽  
Pareto Distributions

Recently, in econophysics, it has been shown that it is possible to analyze economic systems as equilibrium thermodynamic models. We apply statistical thermodynamics methods to analyze income distribution in the Colombian economic system. Using the data obtained in random polls, we show that income distribution in the Colombian economic system is characterized by two specific phases. The first includes about 90% of the interviewed individuals, and is characterized by an exponential Boltzmann-Gibbs distribution. The second phase, which contains the individuals with the highest incomes, can be described by means of one or two power-law density distributions that are known as Pareto distributions.

scholarly journals Deterministic counting of graph colourings using sequences of subgraphs

2020 ◽  
Vol 29 (4) ◽  
pp. 555-586
Author(s):  
Charilaos Efthymiou
Keyword(s):  
Free Energy ◽  
Spatial Correlation ◽  
Random Graph ◽  
Polynomial Time ◽  
Gibbs Distribution ◽  
Correlation Decay ◽  
Point Correlation ◽  
Graph Colourings ◽  
Point To Point

AbstractIn this paper we propose a polynomial-time deterministic algorithm for approximately counting the k-colourings of the random graph G(n, d/n), for constant d>0. In particular, our algorithm computes in polynomial time a $(1\pm n^{-\Omega(1)})$ -approximation of the so-called ‘free energy’ of the k-colourings of G(n, d/n), for $k\geq (1+\varepsilon) d$ with probability $1-o(1)$ over the graph instances.Our algorithm uses spatial correlation decay to compute numerically estimates of marginals of the Gibbs distribution. Spatial correlation decay has been used in different counting schemes for deterministic counting. So far algorithms have exploited a certain kind of set-to-point correlation decay, e.g. the so-called Gibbs uniqueness. Here we deviate from this setting and exploit a point-to-point correlation decay. The spatial mixing requirement is that for a pair of vertices the correlation between their corresponding configurations becomes weaker with their distance.Furthermore, our approach generalizes in that it allows us to compute the Gibbs marginals for small sets of nearby vertices. Also, we establish a connection between the fluctuations of the number of colourings of G(n, d/n) and the fluctuations of the number of short cycles and edges in the graph.

Sign in / Sign up

Export Citation Format

Share Document