Thursday 7 April 2016, 10:15-11:00, Ångström 64119
Anthony Metcalfe,
Uppsala University, Sweden
Universal edge fluctuations of discrete interlaced particle systems
A discrete Gelfand-Tsetlin pattern is a configuration of particles in
Z2.
The particles are arranged in a finite number of consecutive
rows, numbered from the bottom. There is one particle on the first row,
two particles on the second row, three particles on the third row, etc,
and particles on adjacent rows satisfy an interlacing constraint.
In this talk, we consider the uniform probability measure on the set of
all discrete Gelfand-Tsetlin patterns of a fixed size where the particles
on the top row are in deterministic positions. This measure arises
naturally as an equivalent description of the uniform probability measure
on the set of all tilings of certain polygons with lozenges, for example,
the regular hexagon. These systems have a determinantal structure.
We consider the asymptotic behaviour of such systems as the size increases
under the assumption that the empirical distribution of the deterministic
particles on the top row converges weakly. We consider the asymptotic
`shape' of such systems. We provide parameterisations of the asymptotic
boundary (the edge) and investigate the local geometric properties of
the resulting curves. We also consider the local asymptotic behaviour
of particles close to the edge, and we confirm universal edge
asymptotic behaviour for `typical' edge points.
Tuesday
12 April 2016, 13:15-14:00, Ångström 64119
Alexander Vasiliev,
University of Bergen, Norway
Slit holomorphic stochastic flows
We use general Loewner theory to define general slit Loewner chains in
the unit disk, which in the stochastic case lead to slit holomorphic
stochastic flows. Radial, chordal and dipolar SLE are classical examples
of such flows. Our approach, however, allows to construct new processes
of SLE type that possess conformal invariance and some sort of the
domain Markov property. The local behavior of these processes is similar
to that of classical SLEs.
Joint project with Nam-Gyu Kang, George Ivanov and Alexey Tochin
Tuesday
26 April 2016, 13.15-14.00, Ångström 64119
Henning Sulzbach
Convergence and properties of random self-similar trees
In my talk, I discuss real trees arising as scaling limits for random large discrete trees which satisfy a certain distributional self-similarity. The main application is the analysis of limiting objects in the problem of random dissections of the disk. The topics include convergence of compact metric spaces in the so-called Gromov-Hausdorff-Prokhorov topology as well as characterizations of trees by stochastic fixed-point equations. If time permits, I will also present results about their fractal dimensions. The talk will be based on joint work with Nicolas Broutin, INRIA, Paris.
Tuesday
10 May 2016, 13:15-14:00, Ångström 64119
Dimitris Cheliotis
Triangular matrices and biorthogonal ensembles
We discuss distributional properties of the singular values of certain triangular random matrices. For general i.i.d entries, we study the empirical distribution of the singular values, and for certain choices on the distribution of the entries we show their relation with the biorthogonal Laguerre ensemble.
Thursday
12 May 2016, 13:15-14:00, Ångström 64119
Rostyslav Kozhan
Multiplicative non-Hermitian perturbations of Jacobi matrices and of classical random matrix ensembles
We fully classify possible eigenvalue configurations of rank-one
multiplicative non-Hermitian perturbations of Jacobi matrices. We provide a
Hermite-Biehler type theorem for the characteristic polynomial and
an application in random matrix theory.
Since the proof employs just the basic linear algebra and complex analysis,
the talk should be accessible to PhD or even undergraduate students.
This is a joint work with M. Tyaglov.
Tuesday
7 June 2016, 13:15-14:00, Ångström 64119
Achilles Tertikas
On the Hardy constant of non-convex domains
The Hardy constant of a simply connected domain
Ω ∈ ℝn is the best constant c for the inequality
∫Ω |∇ u|2 dx ≥
c ∫Ω
u2 / dist(x,∂Ω)2 dx, u ∈
Cc∞ (Ω).
After the work of Ancona where the universal lower bound 1/16 was obtained for simply connected
planar domains, there has been a substantial interest on computing or estimating the Hardy constant
of simply connected domains.
In this talk I will review on some recent work, on computing Hardy constants of non convex simply
connected domains. Particular attention will be paid on computing Hardy constants of non convex
simply connected planal domains
This is part of a joint work with G Barbatis (University of Athens).
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