This program simulates the vertex-reinforced random walks on arbitrary connected graphs. In this model, each walk has higher probability to visit the vertices which have been less visited by the other walks. Jun (2014) proved that two walks (particles) have small joint support if the repulsion is strong enough in a complete graph.
The vertices are visited by walks that choose the next vertex to be visited according to the number of other walks' visits. Each walk is repelled by the others. The next vertex to be visited has probability inversely proportional to the number of visits of the other walks in it. Self-loops are created by default because the walk can stay at the same place to the next interaction. The program allow the graph patitioning where a set of walks ocupies a complete subgraph.
The program output is a file containing the number walks' visits per time (row) on each vertex.
The project can be downloaded using git as follows:
$ git clone https://github.com/aholanda/rrwg.git
$ cd rrwg
Some tests can be performed by executing:
$ make tests
Before installing the program can be execute in the project directory:
$ ./__main__.py
To install the program and the man page in the system path, just run:
$ sudo make install
To uninstall from system path and clear the current directory from generated files, execute:
$ sudo make uninstall
$ make clean
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Jun Chen. "Two particle's repelling random walks on the complete graph". Eletron. J. Probab. 19 (113), 1--17, 2014.
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Rafael A. Rosales, Fernando P. A. Prado, Benito Pires. "Vertex reinforced random walks with exponential interaction on complete graphs". Stochastic Processes and their Applications 148, 353--379, 2022.