Скачать с ютуб Prof. Peter Clarkson | Matrix Models, Orthogonal Polynomials and Symmetric Freud weights в хорошем качестве

Prof. Peter Clarkson | Matrix Models, Orthogonal Polynomials and Symmetric Freud weights

Speaker: Professor Peter Clarkson (University of Kent) Date: 7th Aug 2024 - 15:00 to 16:00 Venue: External Title: Matrix Models, Orthogonal Polynomials and Symmetric Freud weights Event: (PDW) Emergent phenomena in nonlinear dispersive waves Abstract: Orthogonal polynomials associated with symmetric Freud weights which arise in the context of Hermitian matrix models and random symmetric matrix ensembles, in particular the sextic Freud weight \[ w(x)=\exp\left\{-N \!\left(g_6x^6+ g_4x^4+g_2x^2 \right)\right\},\eqno(1)\] with $N$, $g_6$, $g_4$ and $g_2$ parameters. In the 1990s the behaviour of the recurrence coefficients in the three-term recurrence relation associated with these orthogonal polynomials for the weight (1) was described as being ``chaotic" and more recently the ``chaotic phase" has been interpreted as a dispersive shock. In this talk I will discuss properties of the recurrence coefficients in the three-term recurrence relation associated with these orthogonal polynomials associated with the sextic Freud weight (1). In particular For this weight, the recurrence coefficients satisfy a fourth-order discrete equation which is the second member of the first discrete Painlev\'e hierarchy, and also known as the ``string equation". 👉 Want to learn more about the talks in this stream? 🔗| Seminar Link: https://www.newton.ac.uk/seminar/43997/ 🔗| Programme Link: https://www.newton.ac.uk/event/pdw/ ------------------- FOLLOW US 🌐| Website: https://www.newton.ac.uk 🎥| Main Channel:    / @isaacnewtoninstitute   🐦| Twitter:   / newtoninstitute   💬| Facebook:   / newton.institute   📷| Instagram:   / isaacnewtoninstitute   🔗| LinkedIn:   / isaac-newton-institute-for-mathematical-sc...   SEMINAR ROOMS 🥇| INI Seminar Room 1:    / @iniseminarroom1   🥈| INI Seminar Room 2:    / @iniseminarroom2   🛰️| INI Satellite Events:    / @inisatellite   ABOUT The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period. 👉 Learn more about us and our events here: https://www.newton.ac.uk