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- Title
Multiplicative Renormalization of Stochastic Differential Equations for the Abelian Sandpile Model.
- Authors
Volchenkov, Dimitri
- Abstract
The long-term, large-scale behavior in a problem of stochastic nonlinear dynamics corresponding to the Abelian sandpile model is studied with the use of the quantum-field theory renormalization group approach. We prove the multiplicative renormalization of the model including an infinite number of coupling parameters, calculate an infinite number of renormalization constants, identify a plane of fixed points in the infinite dimensional space of coupling parameters, discuss their stability and critical scaling in the model, and formulate a simple law relating the asymptotic size of an avalanche to a model exponent quantifying the time-scale separation between the slow energy injection and fast avalanche relaxation processes.
- Subjects
RENORMALIZATION group; STOCHASTIC differential equations; ABELIAN groups; NONLINEAR dynamical systems; QUANTUM field theory
- Publication
Dynamics (2673-8716), 2024, Vol 4, Issue 1, p40
- ISSN
2673-8716
- Publication type
Article
- DOI
10.3390/dynamics4010003