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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：Norris, James; Turner, Amanda
作者单位：University of Cambridge; Lancaster University
摘要：We define a new state-space for the coalescing Brownian flow, also known as the Brownian web, on the circle. The elements of this space are families of order-preserving maps of the circle, depending continuously on two time parameters and having a certain weak flow property. The space is equipped with a complete separable metric. A larger state-space, allowing jumps in time, is also introduced, and equipped with a Skorokhod-type metric, also complete and separable. We prove that the coalescing...
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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：Eckhoff, Maren; Kyprianou, Andreas E.; Winkel, Matthias
作者单位：University of Bath; University of Oxford
摘要：Consider a supercritical superdiffusion (X-t)(t >= 0) on a domain D subset of R-d with branching mechanism (x, z) bar right arrow -beta(x)z + alpha(x)z(2) + integral((0, infinity))(e(-zy) - 1 + zy)Pi(x, dy). The skeleton decomposition provides a pathwise description of the process in terms of immigration along a branching particle diffusion. We use this decomposition to derive the strong law of large numbers (SLLN) for a wide class of superdiffusions from the corresponding result for branching...
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作者：Sandier, Etienne; Serfaty, Sylvia
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); New York University
摘要：We study the statistical mechanics of classical two-dimensional Coulomb gases with general potential and arbitrary beta, the inverse of the temperature. Such ensembles also correspond to random matrix models in some particular cases. The formal limit case beta = infinity corresponds to weighted Fekete sets and also falls within our analysis. It is known that in such a system points should be asymptotically distributed according to a macroscopic equilibrium measure, and that a large deviations ...
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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：Gois, B.; Landim, C.
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the Kawasaki dynamics at inverse temperature beta for the Ising lattice gas on a two-dimensional square of length 2L + 1 with periodic boundary conditions. We assume that initially the particles form a square of length n, which may increase, as well as L, with beta. We show that in a proper time scale the particles form almost always a square and that the center of mass of the square evolves as a Brownian motion when the temperature vanishes.
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作者：Sasada, Makiko
作者单位：Keio University
摘要：We give a lower bound on the spectral gap for a class of stochastic energy exchange models. In 2011, Grigo et al. introduced the model and showed that, for a class of stochastic energy exchange models with a uniformly positive rate function, the spectral gap of an N-component system is bounded from below by a function of order N-2. In this paper, we consider the case where the rate function is not uniformly positive. For this case, the spectral gap depends not only on N but also on the average...
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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 ...
