Exact Derivation of a Finite-Size Scaling Law and Corrections to Scaling in the Geometric Galton-Watson Process
| العنوان: | Exact Derivation of a Finite-Size Scaling Law and Corrections to Scaling in the Geometric Galton-Watson Process |
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| المؤلفون: | Garcia-Millan, R., Font-Clos, F. |
| المصدر: | RECERCAT (Dipòsit de la Recerca de Catalunya) Recercat: Dipósit de la Recerca de Catalunya Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) Recercat. Dipósit de la Recerca de Catalunya instname |
| سنة النشر: | 2016 |
| مصطلحات موضوعية: | Matemàtiques, 51 - Matemàtiques |
| الوصف: | The theory of finite-size scaling explains how the singular behavior of thermodynamic quantities in the critical point of a phase transition emerges when the size of the system becomes infinite. Usually, this theory is presented in a phenomenological way. Here, we exactly demonstrate the existence of a finite-size scaling law for the Galton-Watson branching processes when the number of offsprings of each individual follows either a geometric distribution or a generalized geometric distribution. We also derive the corrections to scaling and the limits of validity of the finite-size scaling law away the critical point. A mapping between branching processes and random walks allows us to establish that these results also hold for the latter case, for which the order parameter turns out to be the probability of hitting a distant boundary. |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::5d5f2379d8b2e4836da377afd3b5f4ee http://hdl.handle.net/2072/377764 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.dedup.wf.001..5d5f2379d8b2e4836da377afd3b5f4ee |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |