Postal address: PO Box 80010 3508 TA Utrecht the Netherlands Visiting address: Budapestlaan 6 De Uithof 3584 CD Utrecht room MI 521 Email (with spam prevention): R. Fernandez1 "AT" uu. nl Phone: +31 30-2533732 Fax : +31 30-2518394 Sec. : +31 30 2531430
My main field of research is mathematical statistical mechanics (classical and quantum). In this field I have worked on rigorous determination of critical exponents, non-Gibbs phenomena, uniqueness criteria, convergence of cluster expansions and quantum phase diagrams. I also work in the theory of stochastic processes, with emphasis in chains with long memory. Other topics include perfect simulation algorithms, cutoff and escape behavior in Markov processes and applications of stochastic processes to biological processes and language acquisition.
PhD. in Mathematics, Virginia Polytechnic Institute and State
University (Blacksburg, VA (USA), 1984)
Licenciado en Física, Universidad de Buenos Aires (Buenos Aires,
Argentina, 1976)
Previous positions: Rutgers University, University of Texas at Austin, ETH-Zuerich, EPFL-Lausanne, Universidad de Córdoba (Argentina), Universidade de Sao Paulo (Brazil), Université de Rouen (on leave since mid-2009)
Roberto Fernández, Francesco Manzo, Francesca R. Nardi and Elisabetta Scoppola:
Asymptotically exponential hitting times and
metastability: a pathwise approach without reversibility.
Electronic Journal of Probability, 20, Paper no. 122:1-37, 2016.
(DOI: 10.1214/EJP.v20-3656)
Roberto Fernández, Francesco Manzo, Francesca R. Nardi, Elisabetta Scoppola and Julien Sohier:
Conditioned, quasi-stationary, restricted measures and escape from metastable states.
The Annals of Applied Probability,
26: 760--93, 2016 (DOI 10.1214/15-AAP1102).
Roberto Fernández, Julián Martínez and Frank den Hollander:
Variational description of Gibbs-non-Gibbs dynamical transitions for spin-flip systems with a Kac-type interaction.
J. Stat. Phys. , 156:203--20, 2014.
Roberto Fernández, Julián Martínez and Frank den Hollander:
Variational description of Gibbs-non-Gibbs
dynamical transitions for the Curie-Weiss model.
Commun. Math. Phys., 319: 703--30, 2013.
Roberto Fernández, Sandro Gallo and Grégory Maillard:
Regular g-measures are not always Gibbsian.
Electronic Commun of Probability, 16, paper 64, 2011.
Rodrigo Bissacot, Roberto Fernández, Aldo Procacci and Benedetto Scoppola:
An Improvement of the Lovász Local Lemma via Cluster Expansion.
Accepted for publication at Combinatorics, Probability and Computing.
Aernout C.D. van Enter, Roberto Fernández, Frank den Hollander and Frank Redig:
A large-deviation view on dynamical Gibbs-non-Gibbs transitions.
Moscow Mathematical Journal, 10: 687-711, 2010.
Vincent Deveaux and Roberto Fernández:
Partially ordered models.
J. Stat. Phys., 141: 476-516, 2010
Rodrigo Bissacot, Roberto Fernández, and Aldo Procacci:
On the convergence of cluster expansions for polymer gases.
J. Stat. Phys., 139, pp. 598-617, 2010.
Olivier Bertoncini, Javiera M. Barrera and Roberto Fernández:
Abrupt convergence and escape behavior for birth and death chains.
J. Stat. Phys., 137, pp. 595-623, 2009.
Roberto Fernández, Luiz R. Fontes and Eduardo J. Neves:
Density-Profile Processes Describing Biological Signaling Networks:
Almost Sure Convergence to Deterministic Trajectory.
J. Stat. Phys., 136, pp. 875-901, 2009.
Olivier Bertoncini, Javiera M. Barrera and Roberto Fernández:
Cut-off and exit from metastability: two sides of the same coin.
C. R. Acad. Sci. Paris, Ser. I 346, pp. 69 1-6, 2008.
Tierry de la Rue, Roberto Fernández and Alan D. Sokal:
How to Clean a Dirty Floor: Probabilistic Potential Theory and the Dobrushin Uniqueness Theorem.
Markov Proc. Rel. Fields, 14, pp. 1-78, 2008.
Roberto Fernández and Aldo Procacci:
Regions without complex zeros for chromatic polynomials on
graphs with bounded degree.
Combinatorics Probability and Computing 17, pp. 225-38, 2008.
Roberto Fernández, Aldo Procacci and Benedetto Scoppola:
The analyticity region of the hard sphere gas. Improved bounds.
J. Stat. Phys. 128, pp. 1139-43, 2007.
Roberto Fernández and Aldo Procacci:
Cluster expansion for abstract polymer models. New bounds from an old approach.
Comm. Math. Phys., 274, pp. 123-40, 2007.
Roberto Fernández, Jürg Fröhlich and Daniel Ueltschi:
Mott transition in lattice boson models
Commun. Math. Phys. 266 (2006) 777-95
Roberto Fernández, Grégory Maillard:
Construction of a specification from its singleton part
Alea 2, pp. 297-315, 2006.
Roberto Fernández,
Pablo A. Ferrari,
Gustavo Guerberoff:
Spatial birth-and-death processes in random
environment
Math. Phys. Elect. J. 11, paper 3, 2005.
Roberto Fernández and Grégory Maillard:
Chains with complete connections: General theory,
uniqueness, loss of memory and mixing properties
J. Stat. Phys. 118 (2005) 555-88
Roberto Fernández, Grégory Maillard:
Chains with complete connections and one-dimensional Gibbs
measures
Elect. J. Prob. 9 (2004), 145-76
Roberto Fernández, Arnaud Le Ny and Frank Redig:
Restoration of Gibbsianness for projected and FKG renormalized
measures
Bull. Braz. Math. Soc. 34 (2003) 437-55
Roberto Fernández and Andre Toom: :
Non-Gibbsianness of the
invariant measures of non-reversible cellular automata with totally
asymmetric noise
Asthérisque 287 (2003) 71-87
Roberto Fernández, Arnaud Le Ny and Frank Redig:
Variational
principle and almost quasilocality for some renormalized measures
J. Stat. Phys. 111 (2003) 465--77
Roberto Fernández and Antonio Galves:
Markov approximations of chains of infinite order
Bull. Braz. Math. Soc. 33 (2002) 1--12
Roberto Fernández, Aernout C.D. van Enter and Frank den Hollander,
Frank Redig:
Possible loss and recovery of Gibbsianness during the
stochastic evolution of Gibbs measures
Comm. Math. Phys. 226 (2002) 101-30
Francis Comets, Roberto Fernández,
Pablo A. Ferrari:
Processes with Long Memory: Regenerative Construction and Perfect
Simulation
Ann. App. Probab. 12 (2002) 921--43
Roberto Fernández,
Pablo A. Ferrari,
Nancy L. Garcia:
Perfect simulation for interacting point processes, loss networks and
Ising models
Stoch. Proc. et Appl. 102 (2002) 63-88
Roberto Fernández,
Pablo A. Ferrari,
Nancy L. Garcia:
Loss network representation of Ising contours
Ann. Probab. 29 (2001) 902-37
Nilanjana Datta, Roberto Fernández and Jürg Fröhlich:
Effective Hamiltonians and phase diagrams for tight-binding
models
J. Stat. Phys. 96 (1999) 545-611
Aernout C D van Enter and Roberto Fernández:
Problems with the
definition of renormalized Hamiltonians for momentum-space
renormalization transformations
Phys. Rev. E 59 (1999) 5165-71
Xavier Bressaud, Roberto Fernández and Antonio Galves:
Decay of correlations for non Hölderian dynamics. A coupling
approach
Elect. J. Prob. 4 (1999), Paper no. 3, 1-19
Xavier Bressaud, Roberto Fernández and Antonio Galves:
Speed of $\overline d$-convergence for Markov approximations of
chains with complete connections. A coupling approach
Stoch. Proc. and Appl. 83 (1999) 127-38
Roberto Fernández,
Pablo A. Ferrari,
Nancy L. Garcia:
Measures on contour, polymer or animal models. A probabilistic
approach
Markov Processes and Related Fields 4 (1998), no. 4, 479-97
Aernout C. D. van Enter and Roberto Fernández,
Roberto H. Schonmann,
Senya B. Shlosman:
Complete analyticity of the 2D Potts model above the critical
temperature
Comm. Math. Phys. 189 (1997) 373-93
Roberto Fernández and Charles-Edouard Pfister:
Global specifications and non-quasilocality of projections of
Gibbs measures
Ann. Probab. (1997) 25 1284-315
Nilanjana Datta, Roberto Fernández, Jürg Fröhlich, Luc Rey-Bellet:
Low-Temperature Phase Diagrams of Quantum Lattice
Systems. II. Convergent perturbation expansions and stability in
systems with infinite degeneracy
Helv. Phys. Acta 69 (1996) 752-820
Nilanjana Datta, Roberto Fernández and Jürg Fröhlich:
Low-temperature phase diagrams of quantum lattice systems: I.
stability for quantum perturbations of classical systems with
finitely-many ground states
J. Stat. Phys. 84 (1996) 455-534
Aernout C. D. van Enter, Roberto Fernández, Roman Kotecký:
Pathological behavior of renormalization-group maps at high
fields and above the transition temperature
J. Stat. Phys 79 (1995) 969-92
Aernout C. D. van Enter, Roberto Fernández and
Alan D. Sokal:
Regularity properties and pathologies of position-space
renormalization-group transformations: Scope and limitations of
Gibbsian theory
J. Stat. Phys. 72 (1993) 879-1167
Manuel Asorey, José G. Esteve, Roberto Fernández and Jesús Salas:
Rigorous analysis of renormalization-group pathologies in the
4-state clock model
Nucl. Phys. B392 (1993) 593-618
Aernout C. D. van Enter and Roberto Fernández,
Alan D. Sokal:
Renormalization transformations in the vicinity of first-order
phase transitions: What can and cannot go wrong
Phys. Rev. Lett. 66 (1991) 3253-6
Aernout C. D. van Enter and Roberto Fernández:
A remark on different norms and analyticity for many-particle
interactions
J. Stat. Phys. 56 (1989) 965-72
Roberto Fernández and
Joseph Slawny:
Inequalities and many phase transitions in ferromagnetic
systems
Comm. Math. Phys. 121 (1989) 91-120
Michael Aizenman and Roberto Fernández:
Critical exponents for long-range interactions
Lett. Math. Phys. 16 (1988) 39-49
Michael Aizenman, David Barsky and Roberto Fernández:
The phase transition in a general class of Ising-type models is
sharp
J. Stat. Phys. 47 (1987) 343-74
Michael Aizenman and Roberto Fernández:
On the critical behavior of the magnetization in high dimensional
Ising models
J. Stat. Phys. 44 (1986) 393-454
Roberto Fernández:
Metastability and relaxation of processes. An overview of basic
notions and issues
Markov Proc. Rel. Fields 7 (2000) 5-19
Roberto Fernández and Antonio Galves:
Identifying features in the presence of competing evidence. The case
of first-lanuage acquisition
Dynamical systems: From crystal to chaos (Marseille, 1998),
52-62, World Scientific, 2000
Roberto Fernández:
Random fields in lattices. The Gibbsianness issue
Resenhas do IME-USP 3 (1998) 391-421
Roberto Fernández:
Measures for lattice systems
Physica A 263 (1999) 117-130 (Proceedings of the XXth IUPAP
International Conference on Statistical Physics, Paris, France,
1998).
Aernout C. D. van Enter and Roberto Fernández,
Alan D. Sokal:
Renormalization Transformations: Source of Examples and Problems
in Probability and Statistics
Resenhas do IME-USP 2 (1994) 233-262
(Proceedings for the V CLAPEM, São Paulo, 1993)
Aernout C. D. van Enter and R. Fernández,
Alan D. Sokal:
Non-Gibbsian States for Renormalization-Group Transformations and
Beyond
Cellular Automata and Cooperative Systems,
N. Boccara, E. Goles, S. Martinez, P. Picco, editors; Kluwer,
Dordrecht, 1993, pp. 141-152
[proceedings of the NATO Advanced Studies
Institute workshop on Cellular Automata and Cooperative Systems
(Les Houches 1992)]
Aernout C. D. van Enter and R. Fernández,
Alan D. Sokal:
Non-Gibbsian States
Phase Transitions: Mathematics, Physics, Biology,...
R. Kotecký, editor; World Scientific, Singapore, 1993, pp. 77-84
(proceedings of the 1992 Prague Workshop on Phase Transitions)
Aernout C. D. van Enter and Roberto Fernández,
Alan D. Sokal:
Regularity Properties and Pathologies of Position-Space
Renormalization-Group Transformations
Nucl. Phys. B (Proc. Suppl.) 20 (1991) 48-52.
Roberto Fernández,
Pablo A. Ferrari,
Antonio Galves:
Coupling, renewal and perfect simulation
of chains of infinite order
Notes for a minicourse given
at the V Brazilian School of Probability, Ubatuba, July 30--August 4,
2001
Roberto Fernández:
Contour Ensembles and the Description of Gibbsian
Probability Distributions at Low Temperature
Notes for a
minicourse given at the 21 Colôquio Brasileiro de
Matemática, IMPA, Rio de Janeiro, July 21-25, 1997
Multiculturalismo Intelectual
Revista USP (Universidade de São Paulo), no. 42, junho/agosto
1999, págs. 84-95
Expansion methods in statistical mechanics: Successes, limitations, perspectives and alternatives Utrecht, July 2--3, 2015
Last modified 06-01-2016