- Probability Theory
- Statistical Physics
- Ergodic Theory
- Functional Analysis
Research interests
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Research interests in detail:
Since 1980, I have
worked on a range of topics at the interface between probability theory,
statistical physics, ergodic theory and functional analysis. These
include:
1. fluorescence in photosynthesis
2.
ergodic classification of random sequences
3. large
deviations
4. branching processes in random
environments
5. random walks in static and dynamic random
environments
6. random polymers
7. critical percolation
and invasion percolation
8. metastability under spin-flip and
lattice-gas dynamics
9. transitions between Gibbs and non-Gibbs
under stochastic dynamics
10. intermittency in catalytic random
media
11. interacting diffusions
12.
renormalisation
13. heat conduction in random
domains
14. Wiener sausage.
More recently I am also working on selected topics in
mathematical biology, in particular, population genetics and
immunology.
Since 1990, a common theme in my research
has been the application of large deviation theory to random interacting
systems. My focus has been on the description of phase transitions,
trying to develop new variational techniques.
Research monographs:
(1) F. den Hollander, Large
Deviations, Fields Institute Monographs, Vol. 14, American Mathematical
Society, Providence RI, 2000, x + 143 pp., ISBN 0-8218-1989-5.
AMS has brought out a second print in 2008.
(2) F. den
Hollander, Random Polymers, Lecture Notes in Mathematics, Vol. 1974,
Springer, Berlin, 2009, xiii + 258 pp., ISBN 978-3-642-00332-5.
Based on the lectures I gave at the Saint-Flour Probability School in
July 2007.
(3) A. Bovier and F. den Hollander, Metastability - A Potential-Theoretic Approach, in progress.
Co-authors since 1995:
O. Angel
(Vancouver)
L. Avena (Zuerich)
E. Baake
(Bielefeld)
J.-B. Baillon (Paris)
M. van den Berg
(Bristol)
M. Birkner (Mainz)
M. Biskup (Los
Angeles)
S. Blachere (Utrecht)
E. Bolthausen
(Zuerich)
A. Bovier (Bonn)
F. Caravenna
(Milano)
D. Cheliotis (Athens)
Ph. Clement
(Delft)
P. Dai Pra (Padova)
D. Dawson
(Ottawa)
J. Englaender (Santa Barbara)
A.C.D. van Enter
(Groningen)
R. Fernandez (Utrecht)
J. Gaertner
(Berlin)
A. Gaudilliere (Marseille)
J. Goodman
(Leiden)
A. Greven (Erlangen)
R. van der Hofstad
(Eindhoven)
M.S. Keane (Middletown)
H. Kesten
(Ithaca)
S. Kliem (Eindhoven)
A. Klimovsky
(Eindhoven)
W. Koenig (Berlin)
G. Maillard
(Marseille)
M.V. Menshikov (Durham)
S. Molchanov
(Charlotte)
F.R. Nardi (Eindhoven)
E. Olivieri
(Rome)
A. Opoku (Leiden)
N. Petrelis (Nantes)
F.
Redig (Delft)
R. dos Santos (Leiden)
E. Scoppola
(Rome)
V. Sidoravicius (Rio de Janeiro)
G. Slade
(Vancouver)
C. Spitoni (Leiden)
J.E. Steif
(Gothenburg)
R. Sun (Singapore)
J. Swart
(Prague)
F.-L. Toninelli (Lyon)
A. Troiani
(Leiden)
S. Volkov (Bristol)
S.G. Whittington
(Toronto)
M. Wuethrich (Zuerich)
N. Zint (Bielefeld)