BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Yang Chen (University of Macau)
DTSTART:20221025T130000Z
DTEND:20221025T140000Z
DTSTAMP:20260422T201529Z
UID:CAvid/87
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/87/">L
 aguerre Unitary Ensembles with Multiple Discontinuities\, PDE\, and the Co
 upled Painlevé V System</a>\nby Yang Chen (University of Macau) as part o
 f CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstrac
 t\nWe study the Hankl generated by the Laguerre weight with jump\ndisconti
 nuities at $t_k$\, $k=1\,2\,\\ldots\,m$. By employing the ladder operator 
 approach \nwe establish (multi-time) Riccati equations\, to show that $\\s
 igma_n(t_1\, ...\,t_m)$\,\nthe log derivative of the $n\\times n$ Hankel d
 eterminant\, satisfies a generalization of the $\\sigma$ of a Painlev\\'e 
 V equation. Through investigating the Riemann-Hibert problem (or Homogenou
 s Hilbert Problem )  for the orthogonal polynomials\ngenerated by the LUEM
 D and via Lax pair\, we express $\\sigma_n$ in terms of \nsolutions of a c
 oupled Painlev\\'e V system. We also build relations between the auxiliary
  quantities introduced in the above two methods\, which provide\nconnectio
 ns between the Riccati equations and the Lax Pair. \n\nIn addition\, when 
 each $t_k$ tends to the hard edge of the spectrum and $n$ goes to infinity
 \, the scaled $\\sigma_n$ is shown to satisfy a generalized Painlev\\'e II
 I system.\n\nYang Chen (University of Macau\, Macau)\, Shulin Lyu (Qilu Un
 iversity of Technology\, Shandong Academy of Science)\, Shuai-Xia Xu (Inst
 itut Franco-Chinois  de l'Energie Nculearie\, Sun Yat-sen University\, Gua
 ngzhou\, China\n
LOCATION:https://researchseminars.org/talk/CAvid/87/
END:VEVENT
END:VCALENDAR