Directed polymers on trees: a martingale approach

Buffet, E.; Patrick, A. E.; Pulé, J. V.

doi:10.1088/0305-4470/26/8/011

Cited by 43 publications

(69 citation statements)

References 12 publications

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“…This estimate suggests that the field theory computations of the multifractal dimensions (with replicas, supersymmetry and Liouville field theory) are reliable [8] in the regime |e| < e c . Second, the entropy density for any GREM is known to be self-averaging in the thermodynamic limit [9][10][11][12] and in view of the close connection between GREM and our problem we expect this to be also true here.…”

Section: B |E| < Ecmentioning

confidence: 66%

Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field

et al. 1997

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The multifractal scaling exponents are calculated for the critical wave function of a twodimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into the thermodynamics of a static particle in a random potential. The multifractal exponents are simply given in terms of thermodynamic functions, such as free energy and entropy, which are argued to be self-averaging in the thermodynamic limit. These thermodynamic functions are shown to coincide exactly with those of a Generalized Random Energy Model, in agreement with previous results obtained using Gaussian field theories in an ultrametric space.

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Section: B |E| < Ecmentioning

confidence: 66%

Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field

et al. 1997

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“…[13], which is based on the analogy with the KPP equation and is a non rigorous one, and the approach of Ref. [14], which employs probability theory and is entirely satisfactory from the mathematical point of view. We would like to deal with this type of equation:…”

Section: Discussionmentioning

confidence: 99%

Turbo codes: the phase transition

Montanari

2000

Eur. Phys. J. B

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Turbo codes are a very efficient method for communicating reliably through a noisy channel. There is no theoretical understanding of their effectiveness. In Ref.[1] they are mapped onto a class of disordered spin models. The analytical calculations concerning these models are reported here. We prove the existence of a no-error phase and compute its local stability threshold. As a byproduct, we gain some insight into the dynamics of the decoding algorithm.

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“…The Gibbs inequality tells us then that this average work is at least as large as ∆F = F 1 −F 0 , the increase in free energy. 9 The difference W 0 −∆F is due to the irreversible nature of the abrupt energy injection, and this irreversibility means an increase of the total entropy of the system and its environment, and so, the Gibbs' inequality is, in fact, a version of the second law of thermodynamics. This excess work beyond the free-energy increase, W 0 − ∆F , which can be thought of as the "dissipated work," can easily shown to be equal to kT · D(P 0 P 1 ), where P 0 and P 1 are the canonical distributions pertaining to E 0 and E 1 , respectively.…”

Section: Figurementioning

confidence: 99%

“…It turns out that this model is exactly solvable (in many ways) and one can show (see e.g., [9]) that it admits a glassy phase transition:…”

mentioning

confidence: 99%

Statistical Physics and Information Theory

Merhav

2010

FNT in Communications and Information Theory

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This is a set of lecture notes for a graduate course, which focuses on the relations between Information Theory and Statistical Physics. The course is aimed at EE graduate students in the area of Communications and Information Theory, as well as to graduate students in Physics who have basic background in Information Theory. Strong emphasis is given to the analogy and parallelism between Information Theory and Statistical Physics, as well as to the insights, the analysis tools and techniques that can be borrowed from Statistical Physics and 'imported' to certain problem areas in Information Theory. This is a research trend that has been very active in the last few decades, and the hope is that by exposing the student to the meeting points between these two disciplines, we will enhance his/her background and perspective to carry out research in the field. 2

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Directed polymers on trees: a martingale approach

Cited by 43 publications

References 12 publications

Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field

Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field

Turbo codes: the phase transition

Statistical Physics and Information Theory

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