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Seminario di Probabilità e Finanza Matematica
Mercoledì 8 maggio alle ore 15 nella Sala Riunioni VII piano la Dr.ssa Wioletta Ruszel della Technical University Delft (The Netherlands) terrà un seminario intitolato “Cascades on trees”.
Inspired by experiments in neuroscience studying self-organized critical behaviour in the brain we study the abelian sandpile model on random trees.
It was proven by Dhar and Majumdar (1990) that for the full binary tree (and Bethe lattice) the probability that an avalanche is of size k decays as a power-law with mean-field exponent 3/2.
For the binary and binomial tree, using a transfer matrix approach introduced by Dhar & Majumdar, we prove exponential decay of correlations, and in a small supercritical region (i.e., where the branching process survives with positive probability) exponential decay of avalanche sizes.
This shows a phase transition phenomenon between exponential decay and power law decay of avalanche sizes.
Finally we discuss some extensions and work in progress to avalanche size statistics of sandpile models on Galton-Watson trees.
This is joint work with Antal Jarai, Frank Redig and Ellen Saada.