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We study a class of holomorphic complex measures, which are close in an appropriate sense to a complex Gaussian. We show that these measures can be reduced to a product measure of real Gaussians with the aid of a maximum principle in the complex domain. The formulation of this problem has its origin in the study of a certain class of random Schrödinger operators, for which we show that the expectation value of the Green’s function decays exponentially.

Formalisme thermodynamique

David Ruelle (1975/1976)

Séminaire Bourbaki

From holonomy of the Ising model form factors to $n$ -fold integrals and the theory of elliptic curves.

Boukraa, Salah, Hassani, Saoud, Maillard, Jean-Marie, Zenine, Nadjah (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

From Planck to Ramanujan : a quantum $1 / f$ noise in equilibrium

Michel Planat (2002)

Journal de théorie des nombres de Bordeaux

We describe a new model of massless thermal bosons which predicts an hyperbolic fluctuation spectrum at low frequencies. It is found that the partition function per mode is the Euler generating function for unrestricted partitions $p (n$ ). Thermodynamical quantities carry a strong arithmetical structure : they are given by series with Fourier coefficients equal to summatory functions $σ_{k} (n)$ of the power of divisors, with $k = - 1$ for the free energy, $k = 0$ for the number of particles and $k = 1$ for the internal energy. Low...

From the Lifshitz tail to the quenched survival asymptotics in the trapping problem.

Fukushima, Ryoki (2009)

Electronic Communications in Probability [electronic only]

Functional inequalities and uniqueness of the Gibbs measure — from log-Sobolev to Poincaré

Pierre-André Zitt (2008)

ESAIM: Probability and Statistics

In a statistical mechanics model with unbounded spins, we prove uniqueness of the Gibbs measure under various assumptions on finite volume functional inequalities. We follow Royer's approach (Royer, 1999) and obtain uniqueness by showing convergence properties of a Glauber-Langevin dynamics. The result was known when the measures on the box [-n,n]d (with free boundary conditions) satisfied the same logarithmic Sobolev inequality. We generalize this in two directions: either the constants may be...

Functional integral representations for self-avoiding walk.

Brydges, David C., Imbrie, John Z., Slade, Gordon (2009)

Probability Surveys [electronic only]

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