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96 papers · 1 filter
Convergence of Ising interfaces to Schramm's SLE curves
Dmitry Chelkak, Hugo Duminil-Copin, Clément Hongler +2
We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schramm's SLE…
Crossing probabilities in topological rectangles for the critical planar FK-Ising model
Dmitry Chelkak, Hugo Duminil-Copin, Clément Hongler
We consider the FK-Ising model in two dimensions at criticality. We obtain bounds on crossing probabilities of arbitrary topological rectangles, uniform with respect to the boundar…
Hierarchical model of the actomyosin molecular motor based on ultrametric diffusion with drift
A. Yu. Khrennikov, S. V. Kozyrev, A. Mansson
We discuss the approach to investigation of molecular machines using systems of integro--differential ultrametric (p-adic) reaction--diffusion equations with drift. This approach c…
Intrinsic metric on graded graphs,standardness,and invariant measures
Anatoly Vershik
We define a general notion of a smooth invariant (central) ergodic measure on the space of paths of an -graded graph (Bratteli diagram). It is based on the notion of standardnes…
A new approach to constant term identities and Selberg-type integrals
Gyula Károlyi, Zoltán Lóránt Nagy, Fedor Petrov +1
Selberg-type integrals that can be turned into constant term identities for Laurent polynomials arise naturally in conjunction with random matrix models in statistical mechanics. B…
On modular computation of Groebner bases with integer coefficients
S. Yu. Orevkov
Let be an increasing sequence of ideals of the ring , and let be their union. We propose an algorithm to compute the…