Zobrazeno 1 - 10
of 97
pro vyhledávání: '"Krasovsky, I."'
Publikováno v:
Communications in Mathematical Physics. Aug2023, Vol. 401 Issue 3, p833-894. 62p.
Autor:
Krasovsky, I.
We consider the spectrum of the almost Mathieu operator $H_\alpha$ with frequency $\alpha$ and in the case of the critical coupling. Let an irrational $\alpha$ be such that $|\alpha-p_n/q_n|
Externí odkaz:
http://arxiv.org/abs/1602.08624
Autor:
Claeys, T., Krasovsky, I.
Publikováno v:
Duke Math. J. 164, no. 15 (2015), 2897-2987
We study asymptotic behavior for determinants of $n\times n$ Toeplitz matrices corresponding to symbols with two Fisher-Hartwig singularities at the distance $2t\ge0$ from each other on the unit circle. We obtain large $n$ asymptotics which are unifo
Externí odkaz:
http://arxiv.org/abs/1403.3639
Publikováno v:
Comm. Pure Appl. Math. 66 (2013), 1360-1438
We review some history and some recent results concerning Toeplitz determinants and their applications. We discuss, in particular, the crucial role of the two-dimensional Ising model in stimulating the development of the theory of Toeplitz determinan
Externí odkaz:
http://arxiv.org/abs/1207.4990
We provide an alternative proof of the classical single-term asymptotics for Toeplitz determinants whose symbols possess Fisher-Hartwig singularities. We also relax the smoothness conditions on the regular part of the symbols and obtain an estimate f
Externí odkaz:
http://arxiv.org/abs/1206.1292
Publikováno v:
Bull. Inst. Math. Acad. Sin. (N. S.) 7 (2012), 437-461
The authors analyze the asymptotics of eigenvalues of Toeplitz matrices with certain continuous and discontinuous symbols. In particular, the authors prove a conjecture of Levitin and Shargorodsky on the near-periodicity of Toeplitz eigenvalues.
Externí odkaz:
http://arxiv.org/abs/1110.4089
Autor:
Krasovsky, I.
Publikováno v:
in "New Trends in Mathematical Physics", XVth International Congress on Mathematical Physics, Springer, 2009
We outline an approach recently used to prove formulae for the multiplicative constants in the asymptotics for the sine-kernel and Airy-kernel determinants appearing in random matrix theory and related areas.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/1007.1135
Autor:
Krasovsky, I.
Publikováno v:
Progress in Probability 64 (2011), 305-324
We review the asymptotic behavior of a class of Toeplitz (as well as related Hankel and Toeplitz + Hankel) determinants which arise in integrable models and other contexts. We discuss Szego, Fisher-Hartwig asymptotics, and how a transition between th
Externí odkaz:
http://arxiv.org/abs/1007.1128
Publikováno v:
Int.Math.Res.Notices, Art. ID rnq150 (2010)
We obtain "large gap" asymptotics for a Fredholm determinant with a confluent hypergeometric kernel. We also obtain asymptotics for determinants with two types of Bessel kernels which appeared in random matrix theory.
Comment: 34 pages, 2 figure
Comment: 34 pages, 2 figure
Externí odkaz:
http://arxiv.org/abs/1005.4226
Publikováno v:
Duke Math. J. 160, no. 2 (2011), 207-262
We obtain asymptotic expansions for Toeplitz determinants corresponding to a family of symbols depending on a parameter $t$. For $t$ positive, the symbols are regular so that the determinants obey Szeg\H{o}'s strong limit theorem. If $t=0$, the symbo
Externí odkaz:
http://arxiv.org/abs/1004.3696