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• W2014372326 abstract "We exploit a relation between the mean number $N_{m}$ of minima of random Gaussian surfaces and extreme eigenvalues of random matrices to understand the critical behaviour of $N_{m}$ in the simplest glass-like transition occuring in a toy model of a single particle in $N$-dimensional random environment, with $Ngg 1$. Varying the control parameter $mu$ through the critical value $mu_c$ we analyse in detail how $N_{m}(mu)$ drops from being exponentially large in the glassy phase to $N_{m}(mu)sim 1$ on the other side of the transition. We also extract a subleading behaviour of $N_{m}(mu)$ in both glassy and simple phases. The width $delta{mu}/mu_c$ of the critical region is found to scale as $N^{-1/3}$ and inside that region $N_{m}(mu)$ converges to a limiting shape expressed in terms of the Tracy-Widom distribution." @default.
• W2014372326 created "2016-06-24" @default.
• W2014372326 creator A5011588658 @default.
• W2014372326 creator A5074466389 @default.
• W2014372326 date "2012-10-16" @default.
• W2014372326 modified "2023-10-18" @default.
• W2014372326 title "Critical Behavior of the Number of Minima of a Random Landscape at the Glass Transition Point and the Tracy-Widom Distribution" @default.
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• W2014372326 doi "https://doi.org/10.1103/physrevlett.109.167203" @default.
• W2014372326 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/23215120" @default.
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