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作者：Cerf, Raphael; Dembin, Barbara
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider the standard model of i.i.d. first passage percolation on Z(d) given a distribution G on [0, +infinity] (-infinity is allowed). When G([0, +infinity)) > p(c) (d), it is known that the time constant mu(G) exists. We are interested in the regularity properties of the map G bar right arrow mu(G). We first study the specific case of distributions of the form G(p) = p delta(1) + (1 - p)delta(infinity) for p > p(c) (d). In this case, the travel time between two points is equal to the len...
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作者：Chasapsis, Giorgos; Nayar, Piotr; Tkocz, Tomasz
作者单位：Carnegie Mellon University; University of Warsaw
摘要：We show that the two-dimensional minimum-volume central section of the n-dimensional cross-polytope is attained by the regular 2n-gon. We estab-lish stability-type results for hyperplane sections of l(p)-balls in all the cases where the extremisers are known. Our methods are mainly probabilistic, ex-ploring connections between negative moments of projections of random vec-tors uniformly distributed on convex bodies and volume of their sections.
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作者：Bjornberg, Jakob; Curien, Nicolas; Stefansson, Sigurdur Orn
作者单位：Chalmers University of Technology; University of Gothenburg; Universite Paris Saclay; Institut Universitaire de France; University of Iceland
摘要：We introduce a new familiy of random compact metric spaces S-alpha for alpha is an element of (1, 2), which we call stable shredded spheres. They are constructed from excursions of alpha-stable Levy processes on [0, 1] possessing no negative jumps. Informally, viewing the graph of the Levy excursion in the plane, each jump of the process is cut open and replaced by a circle, and then all points on the graph at equal height, which are not separated by a jump, are identified. We show that the sh...
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作者：Eisenbaum, Nathalie
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
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作者：Bauerschmidt, Roland; Hofstetter, Michael
作者单位：University of Cambridge
摘要：For 0 < beta < 6 pi, we prove that the distribution of the centred maximum of the e-regularised continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted Gumbel distribution as epsilon -> 0. Our proof relies on a strong coupling at all scales of the sine-Gordon field with the Gaussian free field, of independent interest, and extensions of existing methods for the maximum of the lattice Gaussian free field.
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作者：Riera, Armand
作者单位：Universite Paris Saclay
摘要：We consider the model of the Brownian plane, which is a pointed non-compact random metric space with the topology of the complex plane. The Brownian plane can be obtained as the scaling limit in distribution of the uniform infinite planar triangulation or the uniform infinite planar quadrangulation and is conjectured to be the universal scaling limit of many others random planar lattices. We establish sharp bounds on the probability of having a short cycle separating the ball of radius r cente...
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作者：Banerjee, Sayan; Budhiraja, Amarjit
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：The infinite Atlas model describes a countable system of competing Brownian particles where the lowest particle gets a unit upward drift and the rest evolve as standard Brownian motions. The stochastic process of gaps between the particles in the infinite Atlas model does not have a unique stationary distribution and in fact for every a >= 0, pi(a) := circle times(infinity)(i=1) Exp(2 + ia) is a stationary measure for the gap process. We say that an initial distribution of gaps is in the weak ...
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作者：Cannizzaro, Giuseppe; Haunschmid-Sibitz, Levi; Toninelli, Fabio
作者单位：University of Warwick; Technische Universitat Wien
摘要：The present work is devoted to the study of the large time behaviour of a critical Brownian diffusion in two dimensions, whose drift is divergence-free, ergodic and given by the curl of the 2-dimensional Gaussian free field. We prove the conjecture, made in (J. Stat. Phys. 147 (2012) 113-131), according to which the diffusion coefficient D(t) diverges as root/log t for t ->infinity. Start-ing from the fundamental work by Alder and Wainwright (Phys. Rev. Lett. 18 (1967) 988-990), logarithmicall...
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作者：Pimentel, Leandro P. R.
作者单位：Universidade Federal do Rio de Janeiro
摘要：In this article, we consider the KPZ fixed point starting from a two-sided Brownian motion with an arbitrary diffusion coefficient. We apply the integration by parts formula from Malliavin calculus to establish a key relation between the two-point (correlation) function of the spatial derivative process and the location of the maximum of an Airy process plus Brownian motion minus a parabola. Integration by parts also allows us to deduce the density of this location in terms of the second deriv...
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作者：Geng, Xi; Ouyang, Cheng; Tindel, Samy
作者单位：University of Melbourne; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Purdue University System; Purdue University
摘要：This article is concerned with stochastic differential equations driven by a d dimensional fractional Brownian motion with Hurst parameter H > 1/4 and understood in the rough paths sense. Whenever the coefficients of the equation satisfy a uniform hypoellipticity condition, we establish a sharp local estimate on the associated control distance function and a sharp local lower estimate on the density of the solution. Our methodology relies heavily on the rough paths structure of the equation.
