-
作者：Bhattacharya, Sohom; Deb, Nabarun; Mukherjee, Sumit
作者单位：State University System of Florida; University of Florida; University of Chicago; Columbia University
摘要：In this paper we derive a large deviation principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multilinear forms, and number of monochromatic copies of a subgraph. We show that the corresponding rate functions in these cases can be expressed as a variational problem over a suitable space of functions. We use the tools developed to study Gibbs measures with the corresponding Hamiltonians, which include tensor genera...
-
作者：Han, Fang; Huang, Zhihan
作者单位：University of Washington; University of Washington Seattle; University of Pennsylvania
摘要：In their seminal work, Azadkia and Chatterjee ( Ann. Statist. 49 (2021) 3070-3102) initiated graph-based methods for measuring variable dependence strength. By appealing to nearest neighbor graphs based on the Euclidean metric, they gave an elegant solution to a problem of R & eacute;nyi ( Acta Math. Acad. Sci. Hung. 10 (1959) 441-451). This idea was later developed in Deb, Ghosal and Sen (2020) (https://arxiv.org/abs/2010.01768) and the authors there proved that, quite interestingly, Azadkia ...
-
作者：Sadhu, Ritwik; Goldfeld, Ziv; Kato, Kengo
作者单位：Cornell University; Cornell University
摘要：We study statistical inference for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely discrete target distribution. We derive limit distributions for the Lp-error with arbitrary p E [1, oc) and for linear functionals of the empirical OT map, together with their moment convergence. The former has a non-Gaussian limit, whose explicit density is derived, while the latter attains asymptotic normality. Fo...
-
作者：Birkner, Matthias; Callegaro, Alice; Cerny, Jiri; Gantert, Nina; Oswald, Pascal
作者单位：Johannes Gutenberg University of Mainz; Technical University of Munich; University of Basel
摘要：We study a discrete-time branching annihilating random walk (BARW) on the d-dimensional lattice. Each particle produces a Poissonian number of offspring with mean mu which independently move to a uniformly chosen site within a fixed distance R from their parent's position. Whenever a site is occupied by at least two particles, all the particles at that site are annihilated. We prove that for any mu > 1 the process survives when R is sufficiently large. For fixed R we show that the process dies...
-
作者：Margarint, Vlad; Shekhar, Atul; Yuan, Yizheng
作者单位：University of North Carolina; University of North Carolina Charlotte; Tata Institute of Fundamental Research (TIFR); University of Cambridge
摘要：We prove existence (and simpleness) of the trace for both forward and backward Loewner chains under fairly general conditions on semimartingale drivers. As an application, we show that stochastic Komatu-Loewner evolutions SKLE alpha,b are generated by curves. As another application, motivated by a question of A. Sep & uacute;lveda, we show that for alpha > 3/2 and Brownian motion B, the driving function |B-t |(alpha) generates a simple curve for small t. On a related note we also introduce a c...
-
作者：Hening, Alexandru; Qi, Weiwei; Shen, Zhongwei; Yi, Yingfei
作者单位：Texas A&M University System; Texas A&M University Kingsville; University of Alberta
摘要：The present paper is devoted to the study of the long term dynamics of diffusion processes modelling a single species that experiences both demographic and environmental stochasticity. In our setting, the long term dynamics of the diffusion process in the absence of demographic stochasticity is determined by the sign of Lambda(0), the external Lyapunov exponent, as follows: Lambda(0 )< 0 implies (asymptotic) extinction and Lambda(0 )> 0 implies convergence to a unique positive stationary distr...
-
作者：Bristiel, Alexandre; Salez, Justin
作者单位：Universite PSL; Universite Paris-Dauphine; Universite PSL
摘要：We consider activated random walks on arbitrary finite networks, with particles being inserted at random and absorbed at the boundary. Despite the nonreversibility of the dynamics and the lack of knowledge on the stationary distribution, we explicitly determine the relaxation time of the process, and prove that separation cutoff is equivalent to the product condition. We also provide sharp estimates on the center and width of the cutoff window. Finally, we illustrate those results by establish...
-
作者：Hong, Minhao; Liu, Heguang; Xu, Fangjun
作者单位：Shanghai Maritime University; East China Normal University; East China Normal University
摘要：Under certain mild conditions, limit theorems for additive functionals of some d-dimensional self-similar Gaussian processes are obtained. These limit theorems work for general Gaussian processes including fractional Brownian motions, subfractional Brownian motions and bi-fractional Brownian motions. To prove these results, we use the method of moments and an enhanced chaining argument. The Gaussian processes under consideration are required to satisfy certain strong local nondeterminism prope...
-
作者：Djete, Mao fabrice; Touzi, Nizar
作者单位：Universite Paris Cite; Institut Polytechnique de Paris; ENSTA Paris
摘要：We introduce a mean field model for optimal holding of a representative agent of her peers as a natural expected scaling limit from the corresponding N-agent model. The induced mean field dynamics appear naturally in a form which is not covered by standard McKean-Vlasov stochastic differential equations. We study the corresponding mean field game of mutual holding in the absence of common noise. Our first main result provides an explicit equilibrium of this mean field game, defined by a bang-b...
-
作者：Bjornberg, Jakob E.; Mailler, Cecile; Moerters, Peter; Ueltschi, Daniel
作者单位：Chalmers University of Technology; University of Gothenburg; University of Bath; University of Cologne; University of Warwick
摘要：We investigate a disordered variant of Pitman's Chinese restaurant process where tables carry i.i.d. weights. Incoming customers choose to sit at an occupied table with a probability proportional to the product of its occupancy and its weight, or they sit at an unoccupied table with a probability proportional to a parameter 6 > 0. This is a system out of equilibrium where the proportion of customers at any given table converges to zero almost surely. We show that for weight distributions in an...
