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## 2013

### On the existence of a glass transition in a Random Energy Model,

, , , J. Phys. A, (2013), 315002,

### Abstract

We revisit the Random Energy Model by assuming that the energy of each configuration is given by the sum of Nindependent contributions (local energies'') with finite variances,instead of directly assuming a Gaussian energy distribution with a variance proportional to N. Using the large deviation formalism,we find that the glass transition generically exists when local energies have a smooth distribution. In contrast,if the distribution of the local energies has a Dirac mass at the minimal energy,the glass transition may cease to exist. This property is illustrated on a simple example,in which local energies are equal to zero with a finite probability,and positive otherwise.

## 2012

### Renormalization flow for extreme value statistics of random variables raised to a varying power,

, , , J. Phys. A, (2012), 115004,

### Abstract

Using a renormalization approach,we study the asymptotic limit distribution of the maximum value in a set of independent and identically distributed random variables raised to a power $q_n$ that varies monotonically with the sample size $n$. Under these conditions,a non-standard class of max-stable limit distributions,which mirror the classical ones,emerges. Furthermore a transition mechanism between the classical and the non-standard limit distributions is brought to light. If $q_n$ grows slower than a characteristic function $q^*_n$,the standard limit distributions are recovered,while if $q_n$ behaves asymptotically as $\lambda q^*_n$,non-standard limit distributions emerge.