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We discuss a generalization of the conditions of validity of the interpolation method for the density of quenched free energy of mean field spin glasses. The condition is written just in terms of the $L^2$ metric structure of the Gaussian random variables. As an example of application we deduce the existence of the thermodynamic limit for a GREM model with infinite branches for which the classic conditions of validity fail.
The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair $A_1$, $A_2$, where $A_1$ is a hydrodynamic-type Hamiltonian
We generalize Thouless bandwidth formula to its n-th moment. We obtain a closed expression in terms of polygamma, zeta and Euler numbers.
Motivated by fractional quantum Hall effects, we introduce a universal space of statistics interpolating Bose-Einstein statistics and Fermi-Dirac statistics. We connect the interpolating statistics to umbral calculus and use it as a bridge to study t
We consider the generating function of the algebraic area of lattice walks, evaluated at a root of unity, and its relation to the Hofstadter model. In particular, we obtain an expression for the generating function of the n-th moments of the Hofstadt
We study several formulations of zero-mass relativistic equations, stressing similarities between different frameworks. It is shown that all these massless wave equations have fermionic as well as bosonic solutions.