scholarly journals Approximating stationary distributions of fast mixing Glauber dynamics, with applications to exponential random graphs

2019 ◽  
Vol 29 (5) ◽  
pp. 3201-3229
Author(s):  
Gesine Reinert ◽  
Nathan Ross
Keyword(s):  
Random Graphs ◽  
Glauber Dynamics ◽  
Stationary Distributions ◽  
Exponential Random Graphs

scholarly journals PERSISTENCE IN THE ZERO-TEMPERATURE DYNAMICS OF THE Q-STATES POTTS MODEL ON UNDIRECTED-DIRECTED BARABÁSI–ALBERT NETWORKS AND ERDÖS–RÉNYI RANDOM GRAPHS

2008 ◽  
Vol 19 (12) ◽  
pp. 1777-1785 ◽  
Author(s):  
F. P. FERNANDES ◽  
F. W. S. LIMA
Keyword(s):  
Random Graphs ◽  
Potts Model ◽  
Finite Size ◽  
Glauber Dynamics ◽  
The Other ◽  
Finite Size Effect ◽  
Zero Temperature ◽  
Temperature Dynamics ◽  
Short Times ◽  
Q Values

The zero-temperature Glauber dynamics is used to investigate the persistence probability P(t) in the Potts model with Q = 3, 4, 5, 7, 9, 12, 24, 64, 128, 256, 512, 1024, 4096, 16 384, …, 230 states on directed and undirected Barabási–Albert networks and Erdös–Rényi (ER) random graphs. In this model, it is found that P(t) decays exponentially to zero in short times for directed and undirected ER random graphs. For directed and undirected BA networks, in contrast it decays exponentially to a constant value for long times, i.e., P(∞) is different from zero for all Q values (here studied) from Q = 3, 4, 5, …, 230; this shows "blocking" for all these Q values. Except that for Q = 230 in the undirected case P(t) tends exponentially to zero; this could be just a finite-size effect since in the other "blocking" cases you may have only a few unchanged spins.

scholarly journals Metastability for Glauber dynamics on random graphs

2017 ◽  
Vol 27 (4) ◽  
pp. 2130-2158 ◽  
Author(s):  
S. Dommers ◽  
F. den Hollander ◽  
O. Jovanovski ◽  
F. R. Nardi
Keyword(s):  
Random Graphs ◽  
Glauber Dynamics

scholarly journals Phase transitions in exponential random graphs

2013 ◽  
Vol 23 (6) ◽  
pp. 2458-2471 ◽  
Author(s):  
Charles Radin ◽  
Mei Yin
Keyword(s):  
Phase Transitions ◽  
Random Graphs ◽  
Exponential Random Graphs

Finite-size effects in exponential random graphs

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
A Gorsky ◽  
O Valba
Keyword(s):  
Random Graphs ◽  
Ground State ◽  
Size Effects ◽  
Chemical Potential ◽  
Network Flows ◽  
Finite Size ◽  
Critical Value ◽  
Star Model ◽  
Finite Size Effects ◽  
Exponential Random Graphs

Abstract In this article, we show numerically the strong finite-size effects in exponential random graphs. Particularly, for the two-star model above the critical value of the chemical potential for triplets a ground state is a star-like graph with the finite set of hubs at network density $p<0.5$ or as the single cluster at $p>0.5$. We find that there exists the critical value of number of nodes $N^{*}(p)$ when the ground state undergoes clear-cut crossover. At $N>N^{*}(p),$ the network flows via a cluster evaporation to the state involving the small star in the Erdős–Rényi environment. The similar evaporation of the cluster takes place at $N>N^{*}(p)$ in the Strauss model. We suggest that the entropic trap mechanism is relevant for microscopic mechanism behind the crossover regime.

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