Guerra ’ s interpolation using Derrida - Ruelle cascades

نویسندگان

  • Dmitry Panchenko
  • Michel Talagrand
چکیده

New results about Poisson-Dirichlet point processes and Derrida-Ruelle cascades allow us to express Guerra’s interpolation entirely in the language of Derrida-Ruelle cascades and to streamline Guerra’s computations. Moreover, our approach clarifies the nature of the error terms along the interpolation.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Mathematical Aspects of Mean Field Spin Glass Theory

A comprehensive review will be given about the rich mathematical structure of mean field spin glass theory, mostly developed, until now, in the frame of the methods of theoretical physics, based on deep physical intuition and hints coming from numerical simulation. Central to our treatment is a very simple and yet powerful interpolation method, allowing to compare different probabilistic scheme...

متن کامل

Derrida’s Generalised Random Energy models 1: models with finitely many hierarchies

This is the first of a series of three papers in which we present a full rigorous analysis of a class of spin glass models introduces by Derrida under the name of Generalised Random Energy Models (GREM). They are based on Gaussian random processes on the hypercube {−1,1}N with a hierarchical correlation structure. In this first paper we analyse the models with a finite number of hierarchies. In...

متن کامل

The Aizenman-Sims-Starr and Guerra’s schemes for the SK model with multidimensional spins

We prove upper and lower bounds on the free energy of the Sherrington-Kirkpatrick model with multidimensional spins in terms of variational inequalities. The bounds are based on a multidimensional extension of the Parisi functional. We generalise and unify the comparison scheme of Aizenman, Sims and Starr and the one of Guerra involving the GREM-inspired processes and Ruelle’s probability casca...

متن کامل

Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend this argument in order to compare the limiting free energy with the expression given by the Parisi Ansatz, and including full spontaneous replica symmetry br...

متن کامل

The Thermodynamic Limit in Mean Field Spin Glass Models

We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and the Derrida p-spin model. The main argument is based on a smooth interpolation between a large system, made of N spin sites, and two similar but independent su...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007