Central Limit Theorems for the Brownian motion on large unitary groups
نویسنده
چکیده
In this paper, we are concerned with the largeN limit of linear combinations of entries of Brownian motions on the group of N ×N unitary matrices. We prove that the process of such a linear combination converges to a Gaussian one. Various scales of time are concerned, giving rise to various limit processes, in relation to the geometric construction of the unitary Brownian motion. As an application, we recover certain results about linear combinations of the entries of Haar distributed random unitary matrices.
منابع مشابه
Central Limit Theorems and Invariance Principles for Time-One Maps of Hyperbolic Flows
We give a general method for deducing statistical limit laws in situations where rapid decay of correlations has been established. As an application of this method, we obtain new results for time-one maps of hyperbolic flows. In particular, using recent results of Dolgopyat, we prove that many classical limit theorems of probability theory, such as the central limit theorem, the law of the iter...
متن کاملCentral limit theorems for multiple Skorohod integrals
In this paper, we prove a central limit theorem for a sequence of multiple Skorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally Gaussian random variable. Some applications to sequences of multiple stochastic integrals, and renormalized weighted quadratic variation of the fractional Brownian motion are discussed.
متن کاملCentral Limit Theorems and Invariance Principles for Lorenz Attractors
We prove statistical limit laws for Hölder observations of the Lorenz attractor, and more generally for geometric Lorenz attractors. In particular, we prove the almost sure invariance principle (approximation by Brownian motion). Standard consequences of this result include the central limit theorem, the law of the iterated logarithm, and the functional versions of these results.
متن کاملCentral and non-central limit theorems in a free probability setting
Long-range dependence in time series may yield non-central limit theorems. We show that there are analogous time series in free probability with limits represented by multiple Wigner integrals, where Hermite processes are replaced by non-commutative Tchebycheff processes. This includes the non-commutative fractional Brownian motion and the non-commutative Rosenblatt process. AMS subject classif...
متن کاملLimit theorems for the estimation of L integrals using the Brownian motion
We provide a point estimate for integrals on R, based on the standard Brownian motion. We prove the consistency of the estimator and limit theorems for the fluctuations. The proof relies on computing the distribution of the local time of a Brownian motion at a specific stopping time.
متن کامل