31 pagesFor a natural extension of the circular unitary ensemble of order n, we study as n tends to infinity, the asymptotic behavior of the sequence of orthogonal polynomials with respect to the spectral measure. The last term of this sequence is the characteristic polynomial. After taking logarithm and rescaling, we obtain a process indexed by t in [0,1]. We show that it converges to a deterministic limit, and we describe the fluctuations and the large deviations
We study measures generated by systems of linear iterated functions, their Fourier transforms, and t...
We consider the orthogonal polynomials {Pn(z)} with respect to the measure |z − a|2Nce−N|z|2 dA(z) o...
We present a range of fluctuation and large deviations results for the logarithm of the characterist...
31 pagesFor a natural extension of the circular unitary ensemble of order n, we study as n tends to ...
This two-part book is a comprehensive overview of the theory of probability measures on the unit cir...
We consider the orthogonal polynomials with respect to the measure over the whole complex plane. We...
The problem of convergence of the joint moments, which depend on two parameters $s$ and $h$, of the ...
AbstractIn the first five sections, we deal with the class of probability measures with asymptotical...
In the first five sections, we deal with the class of probability measures with asymptotically perio...
In this paper, we consider the asymptotic behavior of X(n)fn≔∑ni=1fn(xi)Xfn(n)≔∑i=1nfn(xi), where xi...
AbstractDefine a discrete measure that attributes masses of size 1/n at every zero of the polynomial...
AbstractThe asymptotic behavior of polynomials that are orthogonal with respect to a slowly decaying...
Abstract: We study the characteristic polynomialsZ(U, θ) of matricesU in the Circular Unitary Ensemb...
We present recent progess on the extremal values of (the logarithm of) the characteristic polynomial...
It is known that a unitary matrix can be decomposed into a product of reflections, one for each dime...
We study measures generated by systems of linear iterated functions, their Fourier transforms, and t...
We consider the orthogonal polynomials {Pn(z)} with respect to the measure |z − a|2Nce−N|z|2 dA(z) o...
We present a range of fluctuation and large deviations results for the logarithm of the characterist...
31 pagesFor a natural extension of the circular unitary ensemble of order n, we study as n tends to ...
This two-part book is a comprehensive overview of the theory of probability measures on the unit cir...
We consider the orthogonal polynomials with respect to the measure over the whole complex plane. We...
The problem of convergence of the joint moments, which depend on two parameters $s$ and $h$, of the ...
AbstractIn the first five sections, we deal with the class of probability measures with asymptotical...
In the first five sections, we deal with the class of probability measures with asymptotically perio...
In this paper, we consider the asymptotic behavior of X(n)fn≔∑ni=1fn(xi)Xfn(n)≔∑i=1nfn(xi), where xi...
AbstractDefine a discrete measure that attributes masses of size 1/n at every zero of the polynomial...
AbstractThe asymptotic behavior of polynomials that are orthogonal with respect to a slowly decaying...
Abstract: We study the characteristic polynomialsZ(U, θ) of matricesU in the Circular Unitary Ensemb...
We present recent progess on the extremal values of (the logarithm of) the characteristic polynomial...
It is known that a unitary matrix can be decomposed into a product of reflections, one for each dime...
We study measures generated by systems of linear iterated functions, their Fourier transforms, and t...
We consider the orthogonal polynomials {Pn(z)} with respect to the measure |z − a|2Nce−N|z|2 dA(z) o...
We present a range of fluctuation and large deviations results for the logarithm of the characterist...
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