April 19  21  26, 2011
STOCHASTIC ACTIVITY MONTH
Mini course:
Maximal Paths in a Class of Stochastic Ordered
Graphs and Related Problems
SERGEY FOSS
VENUE EURANDOM, Green Room, LG 1.105
April 19, 14.30  16.00 h.
April 21, 13.30  15.00 h.
April 26, 13.30  15.00 h.
SPEAKER
Sergey Foss  Heriot Watt
University 
Edinburgh and Institute of
Mathematics  Novosibirsk
Main
Scientific Interests
Stability, Continuity and Optimization Problems for Queueing and
(Tele)Communication Models;, see some "open problems"
Asymptotic Theory of General Stochastic Recursive Sequences and of Markov Chains
and Processes.
Large Deviations in the Presence of Heavy Tails, with Applications
Homepage
ABSTRACT We consider
directed lastpassage percolation on the random graph G=(V,E) where V is the set
of integers and each edge (i,j), for i<j, is present in E independently with
probability p which may depend on the distance ji. To every (i,j), we attach a
random weight v(i,j), and all weights are i.i.d. We study the asymptotics, as n
tends to infinity, for
w(0,n), the maximum weight of all directed paths from 0 to n, and a number of
related problems.
We start with a particular case where the probability p and the weights are
constants. Here we introduce a related model ("infinite bin model") and study
its properties (stability, functional SLLN and CLT, perfect simulation, etc.)
which lead to similar results for our model.
Then we turn to a model with varying probabilities p and use different
techniques for its analysis.
Finally, we consider also random weights v and show that there are essentially
three types of asymptotics, in the cases where (i) the third moment Ev is finite,
(ii) second moment is infinite, and (iii) in then intermediate case.
We also consider a multidimensional analogue of the model.
My lectures are partially based on:
1. S. Foss and T. Konstantopoulos (2003).
Extended renovation theory and limit theorems for stochastic ordered
graphs. Markov Proc. Rel. F., 9, 413468. (can be downloaded from my webpage).
2. D. Denisov, S. Foss, and T. Konstantopoulos.
Limit theorems for a stochastic directed slab graph.
Ann. Appl. Probab. (to appear, can be downloaded from ArXiv).
3. S. Foss, J. Martin, and Ph. Schmidt.
Longrange lastpassage percolation online (working paper)
PROGRAMME
PRACTICAL
INFORMATION
Conference Location
The workshop location is EURANDOM, Den Dolech 2, 5612 AZ
Eindhoven, Laplace Building, 1st floor, LG 1.105.
EURANDOM is located on the campus of
Eindhoven
University of Technology, in the
'Laplacegebouw' building' (LG on the map). The university is located at
10 minutes walking distance from Eindhoven railway station (take the exit
north side and walk towards the tall building on the right with the sign TU/e).
For all information on how to come to Eindhoven, please check http://www.eurandom.tue.nl/contact.htm
Contact
For more information please contact
Mrs. Patty Koorn,
Workshop officer of
EURANDOM
Sponsored by:
STAR
StochasticsTheoretical and
Applied Research
Last updated
180411,
by
PK
