European Institute for Statistics, Probability, Stochastic Operations Research
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April 19 - 21 - 26, 2011


Mini course:

Maximal Paths in a Class of Stochastic Ordered Graphs and Related Problems




EURANDOM mainpage


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.



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


ABSTRACT We consider directed last-passage 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 j-i. 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 multi-dimensional 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, 413-468. (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.
Long-range last-passage percolation online (working paper)





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

For more information please contact Mrs. Patty Koorn,
Workshop officer of  EURANDOM


Sponsored by:

tochastics-Theoretical and Applied Research


Last updated 18-04-11,
by PK