Discretized Diffusion Processes

Details Discretized Diffusion Processes Discretized Diffusion Processes

2000-10-18

arxiv.org/abs/cond-mat/0010253v1

Physics

Condensed Matter

Statistical Mechanics

4 pages 5 figure, to be published in PRL

Scientific paper

10.1103/PhysRevLett.85.4848

We study the properties of the ``Rigid Laplacian'' operator, that is we consider solutions of the Laplacian equation in the presence of fixed truncation errors. The dynamics of convergence to the correct analytical solution displays the presence of a metastable set of numerical solutions, whose presence can be related to granularity. We provide some scaling analysis in order to determine the value of the exponents characterizing the process. We believe that this prototype model is also suitable to provide an explanation of the widespread presence of power-law in social and economic system where information and decision diffuse, with errors and delay from agent to agent.

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