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作者：Edelsbrunner, Herbert; Nikitenko, Anton
作者单位：Institute of Science & Technology - Austria
摘要：Using the geodesic distance on the n-dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the partition of the mosaic into intervals of the radius function and determine the expected number of intervals whose radii are less than or equal to a given threshold. We find that the expectations are essentially the same as for the Poisson-Delaunay mosaic in n-dimensional Euclidean space. Assuming the points are not conta...
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作者：Ding, Xiucai; Yang, Fan
作者单位：University of Toronto; University of Wisconsin System; University of Wisconsin Madison
摘要：In this paper, we prove a necessary and sufficient condition for the edge universality of sample covariance matrices with general population. We consider sample covariance matrices of the form Q = TX(TX)*, where X is an M-2 x N random matrix with X-ij = N-1/2 qij such that qij are i.i.d. random variables with zero mean and unit variance, and T is an M-1 x M-2 deterministic matrix such that T*T is diagonal. We study the asymptotic behavior of the largest eigenvalues of Q when M := min{M-1 x M-2...
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作者：Atar, Rami; Biswas, Anup; Kaspi, Haya; Ramanan, Kavita
作者单位：Technion Israel Institute of Technology; Indian Institute of Science Education & Research (IISER) Pune; Technion Israel Institute of Technology; Brown University
摘要：The Skorokhod map on the half-line has proved to be a useful tool for studying processes with nonnegativity constraints. In this work, we introduce a measure-valued analog of this map that transforms each element. of a certain class of cadlag paths that take values in the space of signed measures on [0, infinity) to a cadlag path that takes values in the space of nonnegative measures on [0, infinity) in such a way that for each x > 0, the path t (bar right arrow) zeta(t) [0, x] is transformed ...
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作者：Crane, Harry
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：Combinatorial Levy processes evolve on general state spaces of combinatorial structures, of which standard examples include processes on sets, graphs and n-ary relations and more general possibilities are given by processes on graphs with community structure and multilayer networks. In this setting, the usual Levy process properties of stationary, independent increments are defined in an unconventional way in terms of the symmetric difference operation on sets. The main theorems characterize b...
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作者：Chenavier, Nicolas; Robert, Christian Y.
作者单位：Universite du Littoral-Cote-d'Opale; Universite Claude Bernard Lyon 1
摘要：We consider the Voronoi tessellation based on a homogeneous Poisson point process in an Euclidean space. For a geometric characteristic of the cells (e.g., the inradius, the circumradius, the volume), we investigate the point process of the nuclei of the cells with large values. Conditions are obtained for the convergence in distribution of this point process of exceedances to a homogeneous compound Poisson point process. We provide a characterization of the asymptotic cluster size distributio...
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作者：Claisse, Julien
作者单位：Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：In this paper, we aim to develop the stochastic control theory of branching diffusion processes where both the movement and the reproduction of the particles depend on the control. More precisely, we study the problem of minimizing the expected value of the product of individual costs penalizing the final position of each particle. In this setting, we show that the value function is the unique viscosity solution of a nonlinear parabolic PDE, that is, the Hamilton-Jacobi-Bellman equation corres...
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作者：El Euch, Omar; Rosenbaum, Mathieu
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However, managing the risks of derivatives under rough volatility can be intricate since the dynamics involve fractional Brownian motion. We show in this paper that surprisingly enough, explicit hedging strategies can be obtained in the case of rough Heston models. The replicating portfolios contain the underl...
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作者：Eldan, Ronen; Gross, Renan
作者单位：Weizmann Institute of Science
摘要：We study the behavior of exponential random graphs in both the sparse and the dense regime. We show that exponential random graphs are approximate mixtures of graphs with independent edges whose probability matrices are critical points of an associated functional, thereby satisfying a certain matrix equation. In the dense regime, every solution to this equation is close to a block matrix, concluding that the exponential random graph behaves roughly like a mixture of stochastic block models. We...
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作者：Beskos, Alexandros; Roberts, Gareth; Thiery, Alexandre; Pillai, Natesh
作者单位：University of London; University College London; University of Warwick; National University of Singapore; Harvard University
摘要：We study the asymptotic behaviour of the Random Walk Metropolis algorithm on ridged probability densities where most of the probability mass is distributed along some key directions. Such class of probability measures arise in various applied contexts including for instance Bayesian inverse problems where the posterior measure concentrates on a manifold when the noise variance goes to zero. When the target measure concentrates on a linear manifold, we derive analytically a diffusion limit for ...
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作者：Cattiaux, Patrick; Delebecque, Fanny; Pedeches, Laure
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse
摘要：In this paper we revisit and generalize various stochastic models extending the deterministic Cucker-Smale model for self-organization. We study flocking and swarming properties. We show how these properties strongly depend on the structure and on the variance of the noise.
