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Thermodynamical Limit for Correlated Gaussian Random Energy Models
"... Let fE (N)g 2N be a family of j N j = 2 random variables de ned by the covariance matrix CN of elements c N (; ) := Av (E (N)E (N)), and HN () = NE (N) the corresponding random Hamiltonian. Then the quenched thermodynamical limit exists if, for every decomposition N = N 1 + N 2 , and a ..."
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, and all pairs (; ) 2 N N : c N (; ) c N1 ( 1 (); 1 ()) + c N2 ( 2 (); 2 ()) where k (); k = 1; 2 are the projections of 2 N into N k . The condition is explicitly verified for the SherringtonKirckpatrick, the even pspin, the Derrida REM and the DerridaGardner GREM models.
Fluctuations of the partition function in the GREM with external field
, 2008
"... We study Derrida’s generalized random energy model in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic limit for all admissible values of parameters. We find that the fluctuations are described by a hierarchica ..."
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We study Derrida’s generalized random energy model in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic limit for all admissible values of parameters. We find that the fluctuations are described by a
ORIGINAL ARTICLE Allelic Depletion of grem1 Attenuates Diabetic Kidney Disease
"... OBJECTIVE—Gremlin (grem1) is an antagonist of the bone morphogenetic protein family that plays a key role in limb bud development and kidney formation. There is a growing appreciation that altered grem1 expression may regulate the homeostatic constraints on damage responses in diseases such as diabe ..."
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such as diabetic nephropathy. RESEARCH DESIGN AND METHODS—Here we explored whether knockout mice heterozygous for grem1 gene deletion (grem1 �/ � ) exhibit protection from the progression of diabetic kidney disease in a streptozotocininduced model of type 1 diabetes. RESULTS—A marked elevation in grem1 expression
Mathematical Physics A Tomography of the GREM: Beyond the REM Conjecture
, 2006
"... Abstract: In a companion paper we proved that in a large class of Gaussian disordered spin systems the local statistics of energy values near levels N1/2+α with α < 1/2 are described by a simple Poisson process. In this paper we address the issue as to whether this is optimal, and what will happe ..."
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will happen if α = 1/2. We do this by analysing completely the Gaussian Generalised Random Energy Models (GREM). We show that the REM behaviour persists up to the level βcN, where βc denotes the critical temperature. We show that, beyond this value, the simple Poisson process must be replaced by more and more
WeierstraßInstitut für Angewandte Analysis und Stochastik Aging in the GREMlike trap model
"... Abstract The GREMlike trap model is a continuous time Markov jump process on the leaves of a finite volume Llevel tree whose transition rates depend on a trapping landscape built on the vertices of the whole tree. We prove that the natural twotime correlation function of the dynamics ages in the ..."
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Abstract The GREMlike trap model is a continuous time Markov jump process on the leaves of a finite volume Llevel tree whose transition rates depend on a trapping landscape built on the vertices of the whole tree. We prove that the natural twotime correlation function of the dynamics ages
On The Generalised Random Energy Model
, 2001
"... The Generalised Random Energy Model is a generalisation of the Random Energy Model introduced by Derrida to mimic the ultrametric structure of the Parisi solution of the SherringtonKirkpatrick model of a spin glass. It was solved exactly in two special cases by Derrida and Gardner. A rigorous anal ..."
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The Generalised Random Energy Model is a generalisation of the Random Energy Model introduced by Derrida to mimic the ultrametric structure of the Parisi solution of the SherringtonKirkpatrick model of a spin glass. It was solved exactly in two special cases by Derrida and Gardner. A rigorous
A QUENCHED LARGE DEVIATION PRINCIPLE AND A PARISI FORMULA FOR A PERCEPTRON VERSION OF THE GREM.
"... ar ..."
CONVEX REPLICA SIMMETRY BREAKING FROM POSITIVITY AND THERMODYNAMIC LIMIT
, 2003
"... Consider a correlated Gaussian random energy model built by successively adding one particle (spin) into the system and imposing the positivity of the associated covariance matrix. We show that the validity of a recently isolated condition ensuring the existence of the thermodynamic limit forces the ..."
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) model including the Derrida REM and the DerridaGardner GREM [2]. In this letter we point out that the proof of [2] may shed some light on the origin of Parisi’s algebraic ansatz for the replica symmetry breaking (RSB) scheme which lies at the basis his solution [3] of the SK model. Algebraically
Derrida’s Generalized Random Energy models 3: Models with continuous hierarchies.
, 2002
"... This is the third of a series of three papers in which we present a rigorous analysis of Derrida's Generalized Random Energy Models (GREM). Here we study the general case of models with a "continuum of hierarchies". We prove the convergence of the free energy and give explicite formul ..."
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This is the third of a series of three papers in which we present a rigorous analysis of Derrida's Generalized Random Energy Models (GREM). Here we study the general case of models with a "continuum of hierarchies". We prove the convergence of the free energy and give explicite
Results 1  10
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1,744