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作者：Bakhtin, Yuri; Chen, Hong-Bin; Pajor-Gyulai, Zsolt
作者单位：New York University
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作者：Banerjee, Sayan; Bhamidi, Shankar
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider models of growing random trees {T-f (n) : n >= 1} with model dynamics driven by an attachment function f : Z(+) -> R+. At each stage a new vertex enters the system and connects to a vertex v in the current tree with probability proportional to f (degree(v)). The main goal of this study is to understand the performance of root finding algorithms. A large body of work (e.g., Random Structures Algorithms 50 (2017) 158-172; IEEE Trans. Netw. Sci. Eng. 4 (2017) 1-12; Random Structures A...
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作者：Forien, Raphael; Pardoux, Etienne
作者单位：INRAE; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：This paper presents a new view of household epidemic models, where we exploit the fact that the interaction between the households is of mean field type. We prove the convergence, as the number of households tends to infinity, of the number of infectious individuals in a uniformly chosen household to a nonlinear Markov process solving a McKean-Vlasov Poisson driven stochastic differential equation, as well as a propagation of chaos result. We also define a basic reproduction number R-* and sho...
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作者：Butez, Raphael; Garcia-Zelada, David
作者单位：University of Geneva; Aix-Marseille Universite
摘要：We study the outliers for two models which have an interesting connection. On the one hand, we study a specific class of planar Coulomb gases which are determinantal. It corresponds to the case where the confining potential is the logarithmic potential of a radial probability measure. On the other hand, we study the zeros of random polynomials that appear to be closely related to the first model. Their behavior far from the origin is shown to depend only on the decaying properties of the proba...
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作者：Bierkens, Joris; Kamatani, Kengo; Roberts, Gareth O.
作者单位：Delft University of Technology; University of Osaka; University of Warwick
摘要：Piecewise deterministic Markov processes are an important new tool in the design of Markov chain Monte Carlo algorithms. Two examples of fundamental importance are the bouncy particle sampler (BPS) and the zig-zag process (ZZ). In this paper scaling limits for both algorithms are determined. Here the dimensionality of the space tends towards infinity and the target distribution is the multivariate standard normal distribution. For several quantities of interest (angular momentum, first coordin...
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作者：Basdevant, Anne-Laure; Gouere, Jean-Baptiste; Theret, Marie
作者单位：Universite de Tours
摘要：We consider the standard model of first-passage percolation on Z(d) (d >= 2), with i.i.d. passage times associated with either the edges or the vertices of the graph. We focus on the particular case where the distribution of the passage times is the Bernoulli distribution with parameter 1 - epsilon. These passage times induce a random pseudo-metric T-epsilon on R-d. By subadditive arguments, it is well known that for any z is an element of R-d \ {0}, the sequence T-epsilon(0, nz)/n converges a...
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作者：Georgiou, Nicholas; Wade, Andrew R.
作者单位：Durham University
摘要：Motivated by nanoscale growth of ultra-thin films, we study a model of deposition, on an interval substrate, of particles that perform Brownian mo-tions until any two meet, when they nucleate to form a static island, which acts as an absorbing barrier to subsequent particles. This is a continuum ver-sion of a lattice model studied in the applied literature. We show that the associated interval-splitting process converges in the sparse deposition limit to a Markovian process (in the vein of Bre...
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作者：Bai, Tianyi; Wan, Yijun
作者单位：New York University; NYU Shanghai; Universite PSL; Ecole Normale Superieure (ENS)
摘要：By introducing a new measure for the infinite Galton-Watson process and providing estimates for (discrete) Green's functions on trees, we establish the asymptotic behavior of the capacity of critical branching random walks: in high dimensions d >= 7, the capacity grows linearly; and in the critical dimension d = 6, it grows asymptotically proportional to n/log n.
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作者：Yasodharan, Sarath; Sundaresan, Rajesh
作者单位：Indian Institute of Science (IISC) - Bangalore
摘要：This paper studies large deviations of a fully coupled finite state meanfield interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment evolves in the fast time scale. Our main result is the path-space large deviation principle for the joint law of the empirical measure process of the particles and the occupation measure process of the fast environment. This extends previous results known for two ...
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作者：Carmona, Rene; Lauriere, Mathieu
作者单位：Princeton University
摘要：We propose two numerical methods for the optimal control of McKean- Vlasov dynamics in finite time horizon. Both methods are based on the intro-duction of a suitable loss function defined over the parameters of a neural net-work. This allows the use of machine learning tools, and efficient implemen-tations of stochastic gradient descent in order to perform the optimization. In the first method, the loss function stems directly from the optimal control problem. The second method tackles a gener...
