7-th Volterra-CIRM International School
Quantum Probability and Spectral Analysis
on Large Graphs
Levico (Trento), Italy, 19 (evening: arrival)-25 (lunch time: departure) September 2004
with the sponsorship of
European Network: QP-Applications
International Association for Quantum Probability and Infinite Dimensional Analysis
The goal of
the school is to discuss the asymptotics of large graphs its applications
physics and to other problems, its connection with other fields of mathematics such as quantum
groups, co-algebras, ...
Emphasis will be on the motivation of the problems and to the use of recently developed quantum
probabilistic techniques, in particular the theory of interacting Fock spaces, in the asymptotic
estimate of the spectrum of the adjacency matrix of large graphs, the possibility of associating
co-products to certain classes of graphs, the connections between graphs and various forms of
The level of the lectures will be suitable for graduate or postgraduate students in physics,
mathematics, information theory..
1) Luigi Accardi, Università di Roma "Tor Vergata"
"Monotone independence, comb graphs and Bose-Einstein condensation"
Burioni, Università di Parma
"Spectral dimension and geometrical universality on graphs"
Hora, Okayama University
"Johnson's graphs and Meixner polynomials"
Kotani, Tohoku University
"Large deviation of random walks and geometry"
"Spectral analysis of transition operators with magnetic potential"
Lenczewski, Wroclaw University
"Coproducts canonically associated to graphs and trees"
Matsui, Kyushu University
"Quantum spin Hamiltonians regarded as elliptic operators on certain graphs"
Obata, Tohoku University
"Interacting Fock spaces and the spectrum of the adjacency matrix of large graphs"
Shirai, Kyushu University
Title to be announced
Sims, University of Newcastle (Australia)
Sodano, Università di Perugia
"Emergence (and stability) of Bose Einstein condensates on inhomogeneous networks"
Vezzani, Università di Parma
"Spectra of graphs and Bose Einstein condensation on inhomogeneous discrete structures "
Additional seminars will be announced later.
The school will be held at Grand Hotel Bellavista in Levico Terme, 20 km. far from Trento. In the heart of the great itineraries between Venice-Verona and Bolzano-Innsbruck, Trento is a Renaissance town in the Alps. Roman town and bridge between the Italian and European culture, Trento shows in its beautiful monuments (the Castle Buonconsiglio, the Duomo, the houses decorated by frescoes) the Renaissance influence, inherited by the Prince Bishops, who ruled the town for eight centuries and made of Trento the seat of the XIX Ecumenical Council during the 16th century.
The conference fee is 400,00 Eur (US $ 486,52). The fee will cover expenses on a full board
basis (night, breakfast, lunch, coffee breaks and dinner) in double accommodation (100,00 Eur
addition for single accommodation) and the social trip on Wednesday afternoon.
It also includes the lecture notes of the main lectures and of the seminars and the right to become
a member of the QP-IDA Association and of receiving the Journal "Infinite Dimensional Analysis,
Quantum Probability and Related Topics" for the year 2005.
Bus transportation will be provided from Trento railway station to the conference site on
Sunday, September 19, at 20:30, and back to Trento railway station on Saturday, September 25.
The deadline for registration is: September 10, 2004.
A restricted number of grants for financial support of either living or (in truly exceptional cases) travel expenses are available. The assignment of these grants will be decided by September 10.
Those interested to apply for such a grant should send via e-mail the Application form to: