scholarly journals Cutoff for the mean-field zero-range process

2019 ◽  
Vol 47 (5) ◽  
pp. 3170-3201 ◽  
Author(s):  
Mathieu Merle ◽  
Justin Salez
Keyword(s):  
Mean Field ◽  
Zero Range Process ◽  
Zero Range ◽  
The Mean ◽  
Range Process

scholarly journals Cutoff for the mean-field zero-range process with bounded monotone rates

2020 ◽  
Vol 48 (2) ◽  
pp. 742-759
Author(s):  
Jonathan Hermon ◽  
Justin Salez
Keyword(s):  
Mean Field ◽  
Zero Range Process ◽  
Zero Range ◽  
The Mean ◽  
Range Process

CONDENSATION ON WEIGHTED NETWORKS WITH SYMMETRIC WEIGHTS

2008 ◽  
Vol 19 (06) ◽  
pp. 927-937 ◽  
Author(s):  
MING TANG ◽  
ZONGHUA LIU ◽  
XIAOYAN ZHU ◽  
XIAOYAN WU
Keyword(s):  
Stationary State ◽  
Mean Field ◽  
Strength Distribution ◽  
Directed Network ◽  
Zero Range Process ◽  
Weighted Networks ◽  
Undirected Network ◽  
Zero Range ◽  
Theoretical Predictions ◽  
Range Process

It is recently shown that the weight-directed network may seriously influence the particle condensation on it, where the weights on an edge are asymmetric. However, most of the realistic networks are weight-undirected networks where the weights on an edge are symmetric. For understanding how the structure of these networks influences the particle evolution, we study the condensation phenomenon on a model of weighted networks with symmetric weights by both theoretical analysis and numerical simulations. In theory, we have proposed a mean field approach to discuss the condensation for the zero range process on weight-undirected networks. We have shown that there is a critical [Formula: see text] and the condensation will occur on the weighted-undirected network for [Formula: see text]. We have also found that the stationary state of particles is determined by the strength distribution, in contrary to the case of asymmetric weights on the edge where the stationary state is determined by the degree distribution. Theoretical predictions are confirmed by two typical weight-undirected networks, where the relationships between the strength and the degree of a node are linear and power law, respectively.

scholarly journals Rate of relaxation for a mean-field zero-range process

2009 ◽  
Vol 19 (2) ◽  
pp. 497-520 ◽  
Author(s):  
Benjamin T. Graham
Keyword(s):  
Mean Field ◽  
Zero Range Process ◽  
Zero Range ◽  
Range Process

scholarly journals Linear response in the nonequilibrium zero range process

2014 ◽  
Vol 64 ◽  
pp. 78-87 ◽  
Author(s):  
Christian Maes ◽  
Alberto Salazar
Keyword(s):  
Linear Response ◽  
Zero Range Process ◽  
Zero Range ◽  
Range Process

The Zero-Range Process

2015 ◽  
pp. 511-541
Author(s):  
Anton Bovier ◽  
Frank den Hollander
Keyword(s):  
Zero Range Process ◽  
Zero Range ◽  
Range Process

scholarly journals A HETEROGENEOUS ZERO-RANGE PROCESS RELATED TO A TWO-DIMENSIONAL WALK MODEL

2012 ◽  
Vol 26 (09) ◽  
pp. 1250044 ◽  
Author(s):  
SEYEDEH RAZIYEH MASHARIAN ◽  
FARHAD H. JAFARPOUR
Keyword(s):  
Partition Function ◽  
Matrix Product ◽  
Two Dimensional ◽  
Canonical Partition Function ◽  
Zero Range Process ◽  
Grand Canonical Partition Function ◽  
Driven Diffusive System ◽  
Zero Range ◽  
Grand Canonical ◽  
Range Process

We have considered a disordered driven-diffusive system defined on a ring. This system can be mapped onto a heterogeneous zero-range process. We have shown that the grand-canonical partition function of this process can be obtained using a matrix product formalism and that it is exactly equal to the partition function of a two-dimensional walk model. The canonical partition function of this process is also calculated. Two simple examples are presented in order to confirm the results.

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