Counting formulas associated with some random matrix averages
نویسندگان
چکیده
Abstract: Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are related to certain configurations of vicious random walkers and to the enumeration of plane partitions. The combinatorial meaning of the average of the characteristic polynomial of random Hermitian and Wishart matrices is also investigated, and consequently several simple universality results are derived.
منابع مشابه
Averages of Characteristic Polynomials in Random Matrix Theory
We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the bulk scaling asymptotic limits are found for ensembles with Gaussian weights. Classical results for the correlation functions of the random matrix ensembles and...
متن کاملA Simple Approach to Global Regime of the Random Matrix Theory
We discuss a method of the asymptotic computation of moments of the normalized eigenvalue counting measure of random matrices of large order. The method is based on the resolvent identity and on some formulas relating expectations of certain matrix functions and the expectations including their derivatives or, equivalently, on some simple formulas of the perturbation theory. In the framework of...
متن کاملAverages of ratios of characteristic polynomials for the compact classical groups
Averages of ratios of characteristic polynomials for the compact classical groups are evaluated in terms of determinants whose dimensions are independent of the matrix rank. These formulas are shown to be equivalent to expressions for the same averages obtained in a previous study, which was motivated by applications to analytic number theory. Our approach uses classical methods of random matri...
متن کاملHeuristics for Fast Exact Model Counting
An important extension of satisfiability testing is model-counting, a task that corresponds to problems such as probabilistic reasoning and computing the permanent of a Boolean matrix. We recently introduced Cachet, an exact model-counting algorithm that combines formula caching, clause learning, and component analysis. This paper reports on experiments with various techniques for improving the...
متن کاملLifted Probabilistic Inference with Counting Formulas
Lifted inference algorithms exploit repeated structure in probabilistic models to answer queries efficiently. Previous work such as de Salvo Braz et al.’s first-order variable elimination (FOVE) has focused on the sharing of potentials across interchangeable random variables. In this paper, we also exploit interchangeability within individual potentials by introducing counting formulas, which i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 113 شماره
صفحات -
تاریخ انتشار 2006