Triangle Seminars
Tuesday, 29 Apr 2008
Extreme Value Statistics, Integer Partitions and Bose Gas
Satya Majumdar
(Paris XI)
Abstract:
In this talk I will first briefly review the extreme value statistics of independent random variables and show how three limiting distributions (Gumbel, Frechet and Weibull distributions) emerge there. Next I'll discuss the celebrated Integer Partition problem of Hardy and Ramanujan and its connection to the ideal Bose gas. We will see how the same three limiting distributions of extreme value statistics appear in the Integer Partion/Bose gas problem. The connection between these three different problems respectively in probability theory, number theory and statistical physics is intriguing and fascinating.
In this talk I will first briefly review the extreme value statistics of independent random variables and show how three limiting distributions (Gumbel, Frechet and Weibull distributions) emerge there. Next I'll discuss the celebrated Integer Partition problem of Hardy and Ramanujan and its connection to the ideal Bose gas. We will see how the same three limiting distributions of extreme value statistics appear in the Integer Partion/Bose gas problem. The connection between these three different problems respectively in probability theory, number theory and statistical physics is intriguing and fascinating.
Posted by: brunel
Wednesday, 30 Apr 2008
The Hamiltonian structure of the second Painleve hierarchy
Marta Mazzocco
(Manchester)
Abstract:
After a short introduction to the Painleve equations, I'll study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear
ODE of order 2n in the independent variable z depending on n
parameters denoted by t(1),...,t(n-1) and alpha(n). I'll
introduce new canonical coordinates and obtain Hamiltonians for the z and t(1),...,t(n-1) evolutions. I'll give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates.
After a short introduction to the Painleve equations, I'll study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear
ODE of order 2n in the independent variable z depending on n
parameters denoted by t(1),...,t(n-1) and alpha(n). I'll
introduce new canonical coordinates and obtain Hamiltonians for the z and t(1),...,t(n-1) evolutions. I'll give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates.
Posted by: brunel
Dynamical Generation of Higher Gauge Groups in Matrix Model.
Subrata Bal
(Dublin)
Abstract:
The dynamics of k coincident D-branes in string theory is described
effectively by U(k) Yang-Mills theory at low energy. While these
configurations appear as classical solutions in matrix models, it was
not clear whether it is possible to realize the k =/= 1 case as the
true vacuum. We consider massive Yang-Mills-Chern-Simons matrix model
and investigate the generation of higher gauge groups U(2), U(3) in
this model.
The dynamics of k coincident D-branes in string theory is described
effectively by U(k) Yang-Mills theory at low energy. While these
configurations appear as classical solutions in matrix models, it was
not clear whether it is possible to realize the k =/= 1 case as the
true vacuum. We consider massive Yang-Mills-Chern-Simons matrix model
and investigate the generation of higher gauge groups U(2), U(3) in
this model.
Posted by: QMW