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作者：Romik, Dan; Sniady, Piotr
作者单位：University of California System; University of California Davis; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Wroclaw
摘要：We study an infinite version of the jeu de taquin sliding game, which can be thought of as a natural measure-preserving transformation on the set of infinite Young tableaux equipped with the Plancherel probability measure. We use methods from representation theory to show that the Robinson Schensted Knuth (RSK) algorithm gives an isomorphism between this measure-preserving dynamical system and the one-sided shift dynamics on a sequence of independent and identically distributed random variable...
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作者：Broutin, Nicolas; Sulzbach, Henning
作者单位：McGill University
摘要：In the recursive lamination of the disk, one tries to add chords one after another at random; a chord is kept and inserted if it does not intersect any of the previously inserted ones. Curien and Le Gall [Ann. Probab. 39 (2011) 2224-2270] have proved that the set of chords converges to a limit triangulation of the disk encoded by a continuous process M. Based on a new approach resembling ideas from the so-called contraction method in function spaces, we prove that, when properly rescaled, the ...
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作者：Geiss, Stefan; Toivola, Anni
作者单位：University of Jyvaskyla; University of Innsbruck
摘要：We consider Gaussian Besov spaces obtained by real interpolation and Riemann-Liouville operators of fractional integration on the Gaussian space and relate the fractional smoothness of a functional to the regularity of its heat extension. The results are applied to study an approximation problem in L-p for 2 <= p < infinity for stochastic integrals with respect to the d-dimensional (geometric) Brownian motion.
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作者：Bolthausen, Erwin; den Hollander, Frank; Opoku, Alex A.
作者单位：University of Zurich; Leiden University; Leiden University - Excl LUMC; Delft University of Technology
摘要：In this paper, we consider a random copolymer near a selective interface separating two solvents. The configurations of the copolymer are directed paths that can make i.i.d. excursions of finite length above and below the interface. The excursion length distribution is assumed to have a tail that is logarithmically equivalent to a power law with exponent alpha >= 1. The monomers carry i.i.d. real-valued types whose distribution is assumed to have zero mean, unit variance, and a finite moment g...
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作者：Bouchard, Bruno; Elie, Romuald; Reveillac, Antony
作者单位：Universite PSL; Universite Paris-Dauphine; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Institut Polytechnique de Paris; ENSAE Paris
摘要：We introduce a new class of backward stochastic differential equations in which the T-terminal value Y-T of the solution (Y, Z) is not fixed as a random variable, but only satisfies a weak constraint of the form E[Psi(Y-T)] >= m, for some (possibly random) nondecreasing map Psi and some threshold m. We name them BSDEs with weak terminal condition and obtain a representation of the minimal time t-values Y-t such that (Y, Z) is a supersolution of the BSDE with weak terminal condition. It provide...
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作者：Hairer, Martin; Hutzenthaler, Martin; Jentzen, Arnulf
作者单位：University of Warwick; Goethe University Frankfurt; Swiss Federal Institutes of Technology Domain; ETH Zurich; Princeton University
摘要：The celebrated Hormander condition is a sufficient (and nearly necessary) condition for a second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficients to be hypoelliptic. As a consequence, the solutions of Kolmogorov PDEs are smooth at all positive times if the coefficients of the PDE are smooth and satisfy Hormander's condition even if the initial function is only continuous but not differentiable. First-order linear Kolmogorov PDEs with smooth coefficients do n...
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作者：Tao, Terence; Vu, Van
作者单位：University of California System; University of California Los Angeles; Yale University
摘要：It is a classical result of Ginibre that the normalized bulk k-point correlation functions of a complex n x n Gaussian matrix with independent entries of mean zero and unit variance are asymptotically given by the determinantal point process on C with kernel K-infinity (z, w):=1/pi e-vertical bar z vertical bar(2)/2-vertical bar w vertical bar(2)/2+z (w) over bar in the limit n ->infinity. In this paper, we show that this asymptotic law is universal among all random n x n matrices M-n whose en...
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作者：Freeman, Nic
作者单位：University of Oxford
摘要：We construct an extension of the A-coalescent to a spatial continuum and analyse its behaviour. Like the A-coalescent, the individuals in our model can be separated into (i) a dust component and (ii) large blocks of coalesced individuals. We identify a five phase system, where our phases are defined according to changes in the qualitative behaviour of the dust and large blocks. We completely classify the phase behaviour, including necessary and sufficient conditions for the model to come down ...
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作者：Camia, Federico; Garban, Christophe; Newman, Charles M.
作者单位：Vrije Universiteit Amsterdam; New York University; New York University Abu Dhabi; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); New York University; Vrije Universiteit Amsterdam; University of California System; University of California Irvine
摘要：The aim of this paper is to prove the following result. Consider the critical Ising model on the resealed grid aZ(2), then the renormalized magnetization field Phi(a) := a(15/8)s Sigma(x is an element of aZ2)sigma(x)delta(x), seen as a random distribution (i.e., generalized function) on the plane, has a unique scaling limit as the mesh size a SE arrow 0. The limiting field is conformally covariant.
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作者：Chen, Lung-Chi; Sakai, Akira
作者单位：Fu Jen Catholic University; Hokkaido University
摘要：We consider long-range self-avoiding walk, percolation and the Ising model on Z(d) that are defined by power-law decaying pair potentials of the form D(x) asymptotic to vertical bar x vertical bar(-d-alpha) with alpha > 0. The upper-critical dimension d(c) is 2(alpha boolean AND 2) for self-avoiding walk and the Ising model, and 3(alpha boolean AND 2) for percolation. Let alpha not equal 2 and assume certain heat-kernel bounds on the n-step distribution of the underlying random walk. We prove ...
