A Self-Interaction Leading to Fluctuations of Order $\boldsymbol{n^{5/6}}$

#### M. Gorny

2015, v.21, Issue 2, 205-248

ABSTRACT

In~\cite{CerfGorny}, we built and studied a Curie\tire Weiss model exhibiting self-organized criticality: it is a model with a self-interaction leading to fluctuations of order $n^{3/4}$ and a limiting law proportional to $\exp(-x^4/12)$. In this paper we modify our model in order to
kill the term $x^4$'' and to obtain a self-interaction leading to fluctuations of order $n^{5/6}$ and a limiting law $C\,\exp(-\lambda x^6)\,dx$, for suitable positive constants $C$ and $\lambda$.

Keywords: Cramer transform, Laplace's method, SOC, critical fluctuations