On statistical mechanics of a single particle in high-dimensional random landscapes
Abstract
We discuss recent results of the replica approach to statistical mechanics of a single classical particle placed in a random N(>>1)-dimensional Gaussian landscape. The particular attention is paid to the case of landscapes with logarithmically growing correlations and to its recent generalisations. Those landscapes give rise to a rich multifractal spatial structure of the associated Boltzmann-Gibbs measure. We also briefly mention related results on counting stationary points of random Gaussian surfaces, as well as ongoing research on statistical mechanics in a random landscape constructed locally by adding many squared Gaussian-distributed terms.
Keywords
Cite
@article{arxiv.0801.0732,
title = {On statistical mechanics of a single particle in high-dimensional random landscapes},
author = {Yan V Fyodorov},
journal= {arXiv preprint arXiv:0801.0732},
year = {2008}
}
Comments
This is mainly a conference presentation summarizing results of arXiv:0706.3776; arXiv:0711.4006 and arXiv:cond-mat/0610035. The work in progress and some new results are briefly discussed in the last part