2 5 M ay 2 00 7 CIRCULAR LAW , EXTREME SINGULAR VALUES AND POTENTIAL THEORY
نویسنده
چکیده
Consider the empirical spectral distribution of complex random n×n matrix whose entries are independent and identically distributed random variables with mean zero and variance 1/n. In this paper, via applying potential theory in the complex plane and analyzing extreme singular values, we prove that this distribution converges, with probability one, to the uniform distribution over the unit disk in the complex plane, i.e. the well known circular law, under the finite fourth moment assumption on matrix elements.
منابع مشابه
Circular law, extreme singular values and potential theory
Consider the empirical spectral distribution of complex random n×n matrix whose entries are independent and identically distributed random variables with mean zero and variance 1/n. In this paper, via applying potential theory in the complex plane and analyzing extreme singular values, we prove that this distribution converges, with probability one, to the uniform distribution over the unit dis...
متن کاملar X iv : 0 80 5 . 34 39 v 1 [ he p - ph ] 2 2 M ay 2 00 8 Single Heavy Flavour Baryons using Coulomb plus Power law interquark Potential
Properties of single heavy flavor baryons in a non relativistic potential model with colour coulomb plus power law confinement potential have been studied. The ground state masses of single heavy baryons and the mass difference between the (JP = 3 2 + and JP = 1 2 + ) states are computed using a spin dependent two body potential. Using the spin-flavour structure of the constituting quarks and b...
متن کاملar X iv : h ep - p h / 04 11 35 2 v 2 2 5 M ay 2 00 5 Electroweak phase transition in an extension of the standard model with a real Higgs singlet
The Higgs potential of the standard model with an additional real Higgs singlet is studied in order to examine if it may allow the strongly first order electroweak phase transition. It is found that there are parameter values for which this model at the one-loop level with finite temperature effect may allow the desired phase transition. Those parameter values also predict that the masses of th...
متن کاملar X iv : p hy si cs / 0 60 52 00 v 1 2 3 M ay 2 00 6 An accurate optical lattice clock with 87 Sr atoms
We report a frequency measurement of the 1S0− 3P0 transition of Sr atoms in an optical lattice clock. The frequency is determined to be 429 228 004 229 879 (5)Hz with a fractional uncertainty that is comparable to state-of-the-art optical clocks with neutral atoms in free fall. Two previous measurements of this transition were found to disagree by about 2× 10, i.e. almost four times the combine...
متن کاملv 2 5 J ul 2 00 5 Non - singular solutions in multidimensional model with scalar fields and exponential potential
Using developed earlier our methods for multidimensional models [1, 2, 3] a family of cosmological-type solutions in D-dimensional model with two sets of scalar fields ϕ and ψ and exponential potential depending upon ϕ is considered. The solutions are defined on a product of n Ricci-flat spaces. The fields from ϕ have positive kinetic terms and ψ are " phantom " fields with negative kinetic ter...
متن کامل