Florian Angeletti

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J. Phys. A

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

F. Angeletti, E. Bertin, P. Abry, J. Phys. A, (2013), 315002,
doi:10.1088/1751-8113/46/31/315002, arxiv:1303.5555, BIB, PDF


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.

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

F. Angeletti, E. Bertin, P. Abry, J. Phys. A, (2012), 115004,
doi:10.1088/1751-8113/45/11/115004, arxiv:1112.2965, BIB, PDF


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.