This MATLAB code allows to simulate the zero-range process on both a one and a two 
dimensional domain (a square box) with potential V. 

In 1D, we consider a periodic boundary (a ring or one-dimensional flat torus). In 2D,
the boundary condition is either zero flux (closed boundary) or a periodic boundary. 
The code provides three different choices for the interacting particles in three 
different folders (see below). Each of these folders contains two `main' files 
which start a simulation with or without detailed balance.

The code was used for the simulations in the paper `Acceleration of convergence to 
equilibrium in Markov chains by breaking detailed balance', J. Stat. Phys.,
DOI 10.1007/s10955-017-1805-z. Detailed explanations of the model and parameter choices 
can be found in the paper.

The zip file contains four folders named `1D', `linear', `sublinear' and `superlinear',
1D is the one-dimensional system. The remaining folders correspond to the 2D model:
The folder `linear' contains the code for simulating independent particles,
the other two versions, `sublinear' and `superlinear' simulate interacting particles with
sublinear and superlinear jump rates.

HOW TO RUN THE PROGRAM:
1D simulation:
Run ZRP1D.m to simulate the particle system with 300 lattice sites in one dimension.

2D simulation:
Within each of the three folders, there is a file ZRP_DB.m which allows to simulate the 
zero-range process satisfying detailed balance, and a file ZRP_nDB.m, which simulates
a zero-range process which does not obey detailed balance.
To run the program, simply run ZRP_DB.m or ZRP_nDB.m.


The remaining .m files are functions which are called by ZRP_DB.m and ZRP_nDB.m

The attached files 

zrp_2d_db_linear.mat
zrp_2d_ndb_linear.mat
zrp_2d_db_sublinear.mat
zrp_2d_ndb_sublinear.mat
zrp_2d_db_superlinear.mat
zrp_2d_ndb_superlinear.mat

are simulation outcomes of running the files ZRP_DB.m and ZRP_nDB.m for each of the 
three cases`linear', `sublinear' and `superlinear'.