Stein’s Method, Heat Kernel, and Traces of Powers of Elements of Compact Lie Groups
نویسنده
چکیده
Combining Stein’s method with heat kernel techniques, we show that the trace of the jth power of an element of U(n, C), USp(n, C) or SO(n, R) has a normal limit with error term of order j/n. In contrast to previous works, here j may be growing with n. The technique should prove useful in the study of the value distribution of approximate eigenfunctions of Laplacians.
منابع مشابه
Stein’s Method and Characters of Compact Lie Groups
Stein’s method is used to study the trace of a random element from a compact Lie group or symmetric space. Central limit theorems are proved using very little information: character values on a single element and the decomposition of the square of the trace into irreducible components. This is illustrated for Lie groups of classical type and Dyson’s circular ensembles. The approach in this pape...
متن کاملLattice of full soft Lie algebra
In this paper, we study the relation between the soft sets and soft Lie algebras with the lattice theory. We introduce the concepts of the lattice of soft sets, full soft sets and soft Lie algebras and next, we verify some properties of them. We prove that the lattice of the soft sets on a fixed parameter set is isomorphic to the power set of a ...
متن کاملHeat Kernel and Moduli Spaces Ii
1. Introduction. In this paper we continue our study on the topology of the moduli spaces of flat bundles on a Riemann surface by using the heat kernels on compact Lie groups. As pointed out in [Liu], our method is very similar to the heat kernel proof of the Atiyah-Bott fixed point formula and the Atiyah-Singer index formula. In our case the local density is given by the Reidemeister torsion o...
متن کاملA Compact Scheme for a Partial Integro-Differential Equation with Weakly Singular Kernel
Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...
متن کاملApplication of Coadjoint Orbits in the Thermodynamics of Non-Compact Manifolds
Method of the solution of the main problem of homogeneous spaces thermodynamics for non-compact spaces in the case of non-compact Lie groups is presented in the article. The method is based on the method of coadjoint orbits. The formula that allows efficiently evaluate heat kernel on non-compact spaces is obtained. The method is illustrated by non-trivial example. c © Electronic Journal of Theo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010