7 A note on Talagrand ’ s positivity principle

A note on Talagrand ' s on entration inequality

A Note on Talagrand’s Positivity Principle

Talagrand’s positivity principle, Section 6.6 in [9], states that one can slightly perturb a Hamiltonian in the Sherrington-Kirkpatrick model in such a way that the overlap of two configurations under the perturbed Gibbs’ measure will become typically nonnegative. In this note we observe that abstracting from the setting of the SK model only improves the result and does not require any modifica...

Thermal Convection in a (Kuvshiniski-type) Viscoelastic Rotating Fluid in the Presence of Magnetic Field through Porous Medium (TECHNICAL NOTE)

  The effect of magnetic field on an incompressible (Kuvshiniski-Type) viscoelastic rotating fluid heated from below in porous medium is considered. For the case of stationary convection, magnetic field and medium permeability have both stabilizing and destabilizing effect on the thermal convection under some conditions whereas rotation has a stabilizing effect on the thermal convection. In the...

Bounds for diluted mean-fields spin glass models

In an important recent paper, [2], S. Franz and M. Leone prove rigorous lower bounds for the free energy of the diluted p-spin model and the K-sat model at any temperature. We show that the results for these two models are consequences of a single general principle. Our calculations are significantly simpler than those of [2], even in the replica-symmetric case.

Exponential inequalities for U-statistics of order two with constants

We wish in these notes to further advance our knowledge of exponential inequalities for U–statistics of order two. These types of inequalities are already present in Hoeffding seminal papers [6], [7] and have seen further development since then. For example, exponential bounds were obtained by Hanson andWright [5] (and the references therein), Bretagnolle [1], and most recently by Giné, Latala,...