[Turkmath:8728] MSGSÜ Genel Seminerleri (4 Ocak)

[Ayse Berkman]

Sayın turkmath Üyeleri,

Bu hafta bölümümüzde iki genel seminer olacaktır. Detaylarını aşağıda
bulabileceğiniz seminerlerimize ilgilenen herkesi bekliyoruz.

Görüşmek dileği ile, selamlar --- Ayşe Berkman

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*4 Ocak 2013 Cuma *

*14.30* Özgür Martin (Miami University at Ohio), "Disjoint Dynamics of
Linear Operators"

*16.00* Atilla Yılmaz (Boğaziçi Üniversitesi), "Harmonic functions and
large deviations for random walk in a random environment"

Yer: MSGSÜ Matematik Bölümü, Seminer Odası

Adres ve harita: http://mat.msgsu.edu.tr/iletisim.html

*Konuşma özetleri:*

**Disjoint Dynamics of Linear Operators, Özgür Martin *

Linear Dynamics is a young and rapidly evolving branch of functional
analysis. It is mainly concerned with the behavior of iterations of linear
transformations. A continuous linear transformation T on a topological
vector space X is said to be hypercyclic provided there is some vector in X
with a dense orbit. Having dense orbits is one of the main ingredients in
the most widely known definitions of chaos.

The aim of this talk is to compare hypercyclicity with the notion of
disjointness introduced by Bernal-Gonzalez and independently by Bes and
Peris. It turns out that some well known results about a single hypercyclic
operator fail to hold true for disjoint hypercyclic operators.

*Harmonic functions and large deviations for random walk in a random
environment, Atilla Yılmaz

Consider random walk in any finite dimension. It has a typical average
velocity. Conditioning it to have some other velocity corresponds to
tilting its transition kernel with some exponential term. This is
formalized in the framework of the theory of large deviations which deals
with exponential rates of decay of probabilities of rare events. The same
connection holds also in the context of random walk in a random environment
(RWRE), except that it is not enough to just tilt the (now random)
transition kernel by a deterministic exponential term. One has to perform
an additional change of measure involving a harmonic function for the
tilted (random) transition kernel. This talk will not assume any prior
knowledge of large deviations or RWRE.
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