2000/10/18 by Stefano Ciliberti, Guido Caldarelli, Paolo De Los Rios +4 · 10 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Applied mathematics #Complex Systems and Time Series Analysis #Computer science #Convergence (economics) #Diffusion #Discretization #Granularity #Laplace operator #Mathematical analysis #Mathematical optimization #Mathematics #Metastability #Operator (biology) #Opinion Dynamics and Social Influence #Physics #Quantum mechanics #Scaling #Set (abstract data type) #Statistical physics #Theoretical and Computational Physics #Truncation (statistics) #Truncation error #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.85.4848
published in Physical Review Letters 85(23), 4848-4851 (American Physical Society) · 4 pages 5 figure, to be published in PRL
arxiv created 2000/10/18 · openalex publication_date 2000/12/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 a social and economic system where information and decision diffuse, with errors and delay from agent to agent.