Proof of the WARM whisker conjecture for neuronal connections

Mark Holmes; Victor Kleptsyn

doi:10.1063/1.4978683

Proof of the WARM whisker conjecture for neuronal connections

Chaos. 2017 Apr;27(4):043104. doi: 10.1063/1.4978683.

Authors

Mark Holmes¹, Victor Kleptsyn²

Affiliations

¹ School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia.
² CNRS, Institute of Mathematical Research of Rennes, Rennes, France.

PMID: 28456154
DOI: 10.1063/1.4978683

Abstract

This paper is devoted to the study of the so-called WARM reinforcement models that are generalisations of Pólya's urn. We show that in the graph setting, once the exponent α of the reinforcement function is greater than 2, the stable and critical equilibria can be supported only on spanning forests, and once α>25, on spanning whisker forests. Thus, we prove the whisker forests conjecture from Hofstad et al. [Ann. Appl. Probab. 26(4), 2494-2539 (2016)].