مورد إلكتروني
On the ratio probability of the smallest eigenvalues in the Laguerre unitary ensemble
| العنوان: | On the ratio probability of the smallest eigenvalues in the Laguerre unitary ensemble |
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| بيانات النشر: | KTH, Matematik (Inst.) IOP PUBLISHING LTD 2018 |
| تفاصيل مُضافة: | Atkin, Max R. Charlier, Christophe Zohren, Stefan |
| نوع الوثيقة: | Electronic Resource |
| مستخلص: | We study the probability distribution of the ratio between the second smallest and smallest eigenvalue in the n x n Laguerre unitary ensemble. The probability that this ratio is greater than r > 1 is expressed in terms of an n x n Hankel determinant with a perturbed Laguerre weight. The limiting probability distribution for the ratio as n -> infinity is found as an integral over (0, infinity) containing two functions q(1)(x) and q(2)(x). These functions satisfy a system of two coupled Painleve V equations, which are derived from a Lax pair of a Riemann-Hilbert problem. We compute asymptotic behaviours of these functions as rx -> 0(+) and (r - 1)x -> infinity, as well as large n asymptotics for the associated Hankel determinants in several regimes of r and x. QC 20180314 |
| مصطلحات الفهرس: | mathematical physics, random matrix theory, Riemann-Hilbert problems, Mathematics, Matematik, Article in journal, info:eu-repo/semantics/article, text |
| DOI: | 10.1088.1361-6544.aa9d57 |
| URL: | Nonlinearity, 0951-7715, 2018, 31:4, s. 1155-1196 |
| الإتاحة: | Open access content. Open access content info:eu-repo/semantics/restrictedAccess |
| ملاحظة: | English |
| أرقام أخرى: | UPE oai:DiVA.org:kth-224002 doi:10.1088/1361-6544/aa9d57 ISI:000425666100002 Scopus 2-s2.0-85045029412 1234922907 |
| المصدر المساهم: | UPPSALA UNIV LIBR From OAIster®, provided by the OCLC Cooperative. |
| رقم الأكسشن: | edsoai.on1234922907 |
| قاعدة البيانات: | OAIster |
| DOI: | 10.1088.1361-6544.aa9d57 |
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