dorsal/arxiv
View SchemaTopology Induced Coarsening in Language Games
| Authors | A. Baronchelli, L. Dall'Asta, A. Barrat, V. Loreto |
|---|---|
| Categories | |
| ArXiv ID | physics/0512045 |
| URL | https://arxiv.org/abs/physics/0512045 |
| DOI | 10.1103/PhysRevE.73.015102 |
| Journal | Phys. Rev. E 73, 015102(R) (2006) |
Abstract
We investigate how very large populations are able to reach a global consensus, out of local "microscopic" interaction rules, in the framework of a recently introduced class of models of semiotic dynamics, the so-called Naming Game. We compare in particular the convergence mechanism for interacting agents embedded in a low-dimensional lattice with respect to the mean-field case. We highlight that in low-dimensions consensus is reached through a coarsening process which requires less cognitive effort of the agents, with respect to the mean-field case, but takes longer to complete. In 1-d the dynamics of the boundaries is mapped onto a truncated Markov process from which we analytically computed the diffusion coefficient. More generally we show that the convergence process requires a memory per agent scaling as N and lasts a time N^{1+2/d} in dimension d<5 (d=4 being the upper critical dimension), while in mean-field both memory and time scale as N^{3/2}, for a population of N agents. We present analytical and numerical evidences supporting this picture.
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"abstract": "We investigate how very large populations are able to reach a global\nconsensus, out of local \"microscopic\" interaction rules, in the framework of a\nrecently introduced class of models of semiotic dynamics, the so-called Naming\nGame. We compare in particular the convergence mechanism for interacting agents\nembedded in a low-dimensional lattice with respect to the mean-field case. We\nhighlight that in low-dimensions consensus is reached through a coarsening\nprocess which requires less cognitive effort of the agents, with respect to the\nmean-field case, but takes longer to complete. In 1-d the dynamics of the\nboundaries is mapped onto a truncated Markov process from which we analytically\ncomputed the diffusion coefficient. More generally we show that the convergence\nprocess requires a memory per agent scaling as N and lasts a time N^{1+2/d} in\ndimension d\u003c5 (d=4 being the upper critical dimension), while in mean-field\nboth memory and time scale as N^{3/2}, for a population of N agents. We present\nanalytical and numerical evidences supporting this picture.",
"arxiv_id": "physics/0512045",
"authors": [
"A. Baronchelli",
"L. Dall\u0027Asta",
"A. Barrat",
"V. Loreto"
],
"categories": [
"physics.soc-ph",
"cond-mat.stat-mech",
"cs.GT",
"cs.MA"
],
"doi": "10.1103/PhysRevE.73.015102",
"journal_ref": "Phys. Rev. E 73, 015102(R) (2006)",
"title": "Topology Induced Coarsening in Language Games",
"url": "https://arxiv.org/abs/physics/0512045"
},
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