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Displaying 21 – 30 of 30

Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices

David Cimasoni (2012)

Journal of the European Mathematical Society

Let $\sum$ be a flat surface of genus $g$ with cone type singularities. Given a bipartite graph $Γ$ isoradially embedded in $\sum$ , we define discrete analogs of the $2^{2 g}$ Dirac operators on $\sum$ . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair $Γ \subset \sum$ for these discrete Dirac operators to be Kasteleyn matrices of the graph $Γ$ . As a consequence, if these conditions are met, the partition function of the dimer...

Disorder relevance at marginality and critical point shift

Giambattista Giacomin, Hubert Lacoin, Fabio Lucio Toninelli (2011)

Annales de l'I.H.P. Probabilités et statistiques

Recently the renormalization group predictions on the effect of disorder on pinning models have been put on mathematical grounds. The picture is particularly complete if the disorder is relevant or irrelevant in the Harris criterion sense: the question addressed is whether quenched disorder leads to a critical behavior which is different from the one observed in the pure, i.e. annealed, system. The Harris criterion prediction is based on the sign of the specific heat exponent of the pure system,...

Disorder relevance for the random walk pinning model in dimension 3

Matthias Birkner, Rongfeng Sun (2011)

Annales de l'I.H.P. Probabilités et statistiques

We study the continuous time version of the random walk pinning model, where conditioned on a continuous time random walk (Ys)s≥0 on ℤd with jump rate ρ > 0, which plays the role of disorder, the law up to time t of a second independent random walk (Xs)0≤s≤t with jump rate 1 is Gibbs transformed with weight eβLt(X,Y), where Lt(X, Y) is the collision local time between X and Y up to time t. As the inverse temperature β varies, the model undergoes a localization–delocalization transition at...

Dissipative systems

Crell, B. (1984)

Proceedings of the 12th Winter School on Abstract Analysis

Duality of Schramm-Loewner evolutions

Julien Dubédat (2009)

Annales scientifiques de l'École Normale Supérieure

In this note, we prove a version of the conjectured duality for Schramm-Loewner Evolutions, by establishing exact identities in distribution between some boundary arcs of chordal ${SLE}_{κ}$ , $κ > 4$ , and appropriate versions of ${SLE}_{\hat{κ}}$ , $\hat{κ} = 16 / κ$ .

Dynamical critical exponent for two-species totally asymmetric diffusion on a ring.

Wehefritz-Kaufmann, Birgit (2010)

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

Dynamical $ℛ$ matrices of elliptic quantum groups and connection matrices for the $q$ -KZ equations.

Konno, Hitoshi (2006)

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

Dynamical sensitivity of the infinite cluster in critical percolation

Yuval Peres, Oded Schramm, Jeffrey E. Steif (2009)

Annales de l'I.H.P. Probabilités et statistiques

In dynamical percolation, the status of every bond is refreshed according to an independent Poisson clock. For graphs which do not percolate at criticality, the dynamical sensitivity of this property was analyzed extensively in the last decade. Here we focus on graphs which percolate at criticality, and investigate the dynamical sensitivity of the infinite cluster. We first give two examples of bounded degree graphs, one which percolates for all times at criticality and one which has exceptional...

Dynamics and Lieb-Robinson estimates for lattices of interacting anharmonic oscillators

L. Amour, P. Lévy-Bruhl, J. Nourrigat (2010)

Colloquium Mathematicae

For a class of infinite lattices of interacting anharmonic oscillators, we study the existence of the dynamics, together with Lieb-Robinson bounds, in a suitable algebra of observables.

Dynamique des nombres et physique des oscillateurs

Jacky Cresson (2008)

Journal de Théorie des Nombres de Bordeaux

Nous présentons un modèle mathématique permettant de reproduire le spectre expérimental des fréquences dans un composant électronique appelé boucle ouverte. Le spectre semble s’organiser suivant une contrainte de nature diophantienne sur les fréquences. Sa structure peut donc se comprendre via une étude de l’ensemble des fractions continues en fonction de leur longueur et de la taille des quotients partiels.

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