Correlations between Zeros and Supersymmetry
نویسنده
چکیده
In our previous work [BSZ2], we proved that the correlation functions for simultaneous zeros of random generalized polynomials have universal scaling limits and we gave explicit formulas for pair correlations in codimensions 1 and 2. The purpose of this paper is to compute these universal limits in all dimensions and codimensions. First, we use a supersymmetry method to express the n-point correlations as Berezin integrals. Then we use the Wick method to give a closed formula for the limit pair correlation function for the point case in all dimensions.
منابع مشابه
ar X iv : m at h - ph / 0 01 10 16 v 1 1 0 N ov 2 00 0 CORRELATIONS BETWEEN ZEROS AND SUPERSYMMETRY
We complete the computations in [BSZ2] and give a supersymmetric formula for the scaling limit correlation functions for simultaneous zeros of generalized polynomials. We also give an explicit formula for the scaling limit pair correlation function for the point case in all dimensions.
متن کاملCorrelations between Zeros of a Random Polynomial
We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval (−1, 1) are asymptotically independent of the zeros outside of this interval, and that the straightened zeros have the same limit translation invariant correlations. Then we calculate the correlations between the straightened zeros of the SO(2) random p...
متن کاملFurther Observations on Blocking Zeros in Linear Muitivariabie systems (RESEARCH NOTE).
While attempting to clarify the confusion concerning the conceptualization of "blocking zeros" in state space in the recent literature, some new observations are made on the relationship between pole-zero cancellation and transmission blocking. An important distinction between uncontrollable and unobservable eigenvalue s is pointed out; and it is argued that the description of a Blocking Zero, ...
متن کاملCorrelations of Zeros and the Distribution of Almost Primes
We establish relationships between mean values of products of logarithmic derivatives of the Riemann zeta-function near the critical line, correlations of the zeros of the Riemann zeta-function and the distribution of integers representable as a product of a fixed number of prime powers.
متن کاملar X iv : m at h - ph / 0 10 30 37 v 1 2 6 M ar 2 00 1 SU ( 1 , 1 ) Random Polynomials
We study statistical properties of zeros of random polynomials and random analytic functions associated with the pseudoeuclidean group of symmetries SU(1, 1), by utilizing both analytical and numerical techniques. We first show that zeros of the SU(1, 1) random polynomial of degree N are concentrated in a narrow annulus of the order of N around the unit circle on the complex plane, and we find ...
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 2001