The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach [0.03%]
多边际嵌入问题的根解：最优停止和时间反演方法
Alexander M G Cox,Jan Obłój,Nizar Touzi
Alexander M G Cox
We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal argum...
Dmitry Beliaev,Igor Wigman
Dmitry Beliaev
We study the volume distribution of nodal domains of families of naturally arising Gaussian random fields on generic manifolds, namely random band-limited functions. It is found that in the high energy limit a typical instance obeys a deter...
Mathias Beiglböck,Manu Eder,Christiane Elgert et al.
Mathias Beiglböck et al.
We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times τ of Brownian motion subject to the constraint that the distribution of τ is a given...
Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation [0.03%]
三立方次非线性薛定谔方程的准不变高斯测度
Tadahiro Oh,Nikolay Tzvetkov
Tadahiro Oh
We consider the cubic fourth order nonlinear Schrödinger equation on the circle. In particular, we prove that the mean-zero Gaussian measures on Sobolev spaces [Formula: see text], [Formula: see text], are quasi-invariant under the flow. ...
Francesco Caravenna,Rongfeng Sun,Nikos Zygouras
Francesco Caravenna
Any renewal processes on [Formula: see text] with a polynomial tail, with exponent [Formula: see text], has a non-trivial scaling limit, known as the [Formula: see text]-stable regenerative set. In this paper we consider Gibbs transformatio...
Optimal Estimation and Rank Detection for Sparse Spiked Covariance Matrices [0.03%]
稀疏发散型协方差矩阵的最优估计和秩检测
Tony Cai,Zongming Ma,Yihong Wu
Tony Cai
This paper considers a sparse spiked covariancematrix model in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of co...