The Alp-Workshop is meant to
bring together people from probability theory and
the spectral theory of operators. The goal of the
workshop is a discussion concerning random graphs
from the viewpoint of either of these two fields.
Probabilistic aspects of the graph's randomness
(e.g. independence, stationarity) and the nature of
the random walk (e.g. recurrence) are opposed to
spectral properties of the corresponding Laplacians
(e.g. spectral radius, type of spectrum, density of
states).
In particular, spectral properties of percolation
models and Erdös-Renyi random graphs will be among
the fields of interest.
The workshop will take place right after the 'Workshop
on Boundaries', which is held in Graz
between June 29th and July 4th.
Models of discrete probability theory such as
percolation and random networks have, apart from
their probabilistic content, a natural relationship
to the spectral theory of linear operators. For
example, the question of the nature of the spectrum
of the Laplacian associated with a specific random
walk on lamplighter groups has recently been shown
to have a counterpart in percolation theory. On the
other hand, the now classical problem of the random
walk in random environment appears in the guise of
the study of ergodic Jacobi matrices - mostly
studied in mathematical physics. Old and new
problems both of probability and spectral theory
have common ground - at the alp-workshop, experts of
both communities shall join in an ideal environment
for an exchange of ideas.
