String Theory Seminars
Quantum Mechanics of Plancherel Growth (Quantum Spacetime Seminar Series)
by Dr. Neetu (IISER Bhopal)
Monday, February 3, 2020 from to (Asia/Kolkata)
at A 304
at A 304
Growth of Young diagrams, equipped with Plancherel measure, follows the automodel equation of Kerov. Using the technology of unitary matrix model I will show that such growth process is exactly the same as the growth of gap less phase of Gross-Witten and Wadia (GWW) model. The analysis offers an alternate proof of limit shape theorem of Vershik-Kerov and Logan-Shepp. I will discuss about large N fluctuations of Young diagrams. Quantization of fluctuations using Hamiltonian dynamics shows that the modes of fluctuations satisfy an abelian Kac-Moody algebra. Eventually, I will propose a correspondence between states of Hilbert space and automodel diagrams, inspired by the quantization procedure.