Workshop on Mathematical Physics

Mambucaba, August 19 – 25, 2001

  • Anderson Localization, Classical and Quantum Spin Systems
  • Critical Percolation and Conformally Invariant Processes
  • Disordered Systems, Polymers and Random Walks in Random Environment
  • Homogenization and granular media

 

The goals of the workshop are to bring together researchers in mathematical physics, probability, dynamical systems, complex analysis and combinatorics, to describe recent results and methods, and promote future advances.

Plenty of time will be reserved for informal interaction among participants. Weather in the region in August is usually very pleasant, and one afternoon will be left free, allowing participants to enjoy the area, boat excursion or to visit the historical city of Paraty.

 

Scientific Committee

A. Klein, UC – Irvine
C.M. Newman, Courant Inst.
R. Schonmann, UCLA
V. Sidoravicius, IMPA
H. Spohn, TU-München
A.-S. Sznitman, ETH
 

Organizers

Abel Klein
Vladas Sidoravicius.

 

 

Schedule

 

Time/Date Monday Tuesday Wednesday Thursday Friday Saturday
8:00 – 9:45 Gibbs Phase Rule for a Particle System in Rd
E. Presutti
Conformal Invariance of Critical Percolation
S. Smirnov
  3D Young Diagrams and the 3D Ising Wulff Crystal at Low Temperature
R. Cerf
TBA
M. Aizenman
Oriented Percolation in a Dependent Environment
M.E. Vares
9:50 – 10:35 Stochastic Löwner Evolution and the Self-Avoiding Walk
G. Lawler
Ergodicity of 2D Turbulence
A. Kupiainen
  Morphology of Dunes
H. Herrmann
Kraichnan Caricature of Turbulence and Stochastic Flows
Y. Le Jan
TBA
J-M. Combes
10:35 – 10:55 Coffee Break
10:55 – 11:40 Sticky Particle Systems with Random Initial Velocities
J. Bertoin
Triviality of Hierarchical Ising Model in Four Dimensions
T. Hara
  Stretched Exponential Fixation in Stochastic Ising Models at Zero Temperature
V. Sidoravicius
Spectral Theory and Oscillatory Integrals in Non-Linear Wave Interaction
A. Figotin
Asymptotics of Equilibrium Probabilities for a Random Walk in One-Eight of a Square Lattice
Y. Suhov
11:45 – 12:30 Non-Uniformly Hyperbolic Horseshoes
J-C. Yoccoz
Green’s Function Estimates for Lattice Schrödinger Operators and the Kicked Rotor Problem
J. Bourgain
  Rigorous Results in the Mean Field Spin Glass Model
F. Guerra
On the Scaling Behavior of Certain Quantities in Regular and Invasion Percolation
A. Pisztora
TBA
B. Duplantier
12:30 – 16:15 Lunch
16:15 – 17:00 Motion of a Particle in a Random Medium
E. Cohen
Nonextensive Statistical Mechanics – What Can We Do with Kolmogorov-Sinai Entropy, Lyapunov Exponents and Related Concepts at the Edge of Chaos?
C. Tsallis
Approach to Equilibrium for a Forced Burgers Equation
W. Kirsch
(16:00 -16:45)
Positive Lyapunov Exponents and Continuity of Spectra of Quasiperiodic Operators
S. Jitomirskaya
The Integrated Density of States for Some Random Operators on Rd
P. Hislop
 
17:00 – 17:15 Coffee Break Coffee Break
(17:35 – 17:50)


Spectral Analysis of Weakly Coupled Stochastic Lattice Ginzburg-Landau Models
P. Da Veiga
(17:50 – 18:35)
Coffee Break
17:15 – 18:00 The Insulator Regime for Random Schrödinger Operators
A. Klein
Quenched-Annealed Transition for Some Stochastic Processes in Random Environment
A. F. Ramírez
Critical Probability Bounds for Archimedian Lattices
J. Wierman
(16:50 -17:35)
Lower Bounds for N-Particle Hamiltonians
M. O’Carroll
Hyperbolicity of Renormalization for CrUnimodal Maps
E. de Faria
 
18:05 – 18:50 Order Parameter for the Anderson Metal-Insulator Transport Transition
F. Germinet
Critical Behavior of the Two-Dimensional Ising Model at the Boundary of a Half-Infinite Cylinder
Y. Saint-Aubin
Localization and Delocalization in Random Polymer Chains
G. Stolz
(18:40 – 19:25)


Small Break
(19:25 – 19:35)
Weak Disorder Localization and Lifshitz Tails
F. Klopp
Supersymmetry and Spectral Theory of Random Schrödinger Operators
W-M. Wang
 
19:00 -20:35

S e s s i o n s

 

Pleanry

Errico Presutti  (Univ. di Roma  Tor Vergata) – Gibbs phase rule for a particle system in Rd
Gregory Lawler   (Duke Univ) – Stochastic Löwner evolution and the self-avoiding walk
Jean Bertoin  (Univ. Paris VI) – Sticky particle systems with Random initial velocities
Jean-Christophe Yoccoz   (Collège de France) – Non-uniformly hyperbolic horseshoes
Eddie Cohen  (The Rockefeller Univ.) – Motion of a particle in a Random medium
Abel Klein  (Univ. of Cal.  Irvine) – The insulator regime for Random Schrödinger operators
François Germinet  (Univ. de Lille 1) – Order parameter for the Anderson metal-insulator transport transition
Stanislav Smirnov  (KTH  Royal Inst.Tech) – Conformal invariance of critical percolation
Antti Kupiainen  (Univ. of Helsinki) – Ergodicity of 2D turbulence
Takashi Hara  (Nagoya Univ.) – Triviality of hierarchical ising model in four dimensions
Jean Bourgain  (IAS  Princeton) – Green’s function estimates for lattice Schrödinger operators and the kicked rotor problem
Constantino Tsallis  (CBPF) – Nonextensive statistical mechanics – what can we do with Kolmogorov-Sinai entropy  Lyapunov exponents and related concepts at the edge of Chaos?
Alejandro Ramirez  (Pontificia Univ. Católica do Chile) – Quenched-annealed transition for some stochastic processes in Random environment
Yvan Saint-Aubin (Univ. Montreal) – Critical behavior of the two-dimensional ising model at the boundary of a half-infinite cylinder
Werner Kirsch (Ruhr Univ. Bochum) – Approach to equilibrium for a forced Burgers equation
John Wierman (John Hopkins Univ.) – Critical probability bounds for archimedian lattices
Gunter Stolz (Univ. Alabama, Birminghan) – Localization and delocalization in Random polymer chains
Raphael Cerf (Univ. Paris-Sud, Orsay) –  3D young diagrams and the 3D ising  Wulff crystal at low temperature
Svetlana Jitomirskaya (Univ. of Cal, Irvine) –  Positive Lyapunov exponents and continuity of spectra of quasiperiodic operators
Vladas Sidoravicius (IMPA) –  Stretched exponential fixation in stochastic ising models at zero temperature
Francesco Guerra (Univ. di Roma, La Sapienza) –  Rigorous results in the mean field Spin glass model
Paulo da Veiga (USP de S. Carlos) –  Spectral analysis of weakly coupled stochastic lattice Ginzburg-Landau  models
Frederic Klopp (Univ. Paris-Nord) –  Weak disorder localization and Lifshitz tails
Michael O’Carroll (Univ.Fed. Minas Gerais) –  Lower bounds for N-particle Hamiltonians
Michael Aizenman (Princeton Univ) – On some statistic-mechanical aspects of the Anderson localization
Yves Le Jan (Univ. Paris Sud) – Kraichnan caricature of turbulence and stochastic flows
Alex Figotin (Univ. Cal., Irvine)  – Spectral theory and oscillatory integrals in non-linear wave interaction
Agoston Pisztora (Carnegie-Mellon University) – On the scaling behavior of certain quantities in regular and invasion percolation
Peter Hislop (Univ. of Kentucky) – The integrated density of states for some Random operators on Rd
Domingos Marchetti (IME/USP) – Complex function characterization of measures possessing Lee-Yang property
Wei-Min Wang (Univ. Paris Sud – Orsay) – Supersymmetry and spectral theory of Random Schrödinger operators
Maria Eulália Vares (IMPA) – Oriented percolation in a dependent environment
Jean-Michel Combes (Centre de Physique Theorique, Luminy) – Properties of Quantum Hall Hamiltonians
Yurii Suhov (Univ. of Cambridge) – Asymptotics of equilibrium probabilities for a Random walk in one-eight of a square lattice

 

Sessions

David Damanik  (Univ. of Cal.  Irvine) – Spectral and dynamical properties of sturmian Hamiltonians
Federico Camia  (Courant Inst.-NYU) – Cluster structure in zero-temperature stochastic ising model
Cesar R. de Oliveira  (UFSCAR) – Spectrum of almost periodic dimers
Gustavo A. da Costa  (Univ. Fed. Sta.Catarina) – Feynman identity:  A special case
José Ramirez  (Cornell University) – Short time asymptotics of symmetric semigroups associated with local dirichlet forms
Giovani Vasconcelos  (Univ.Fed.Pernambuco) – Large geometrical models for granular flow
Michael Campbell (Univ. Cal.  Irvine) – Energy correlations in O(N) models and the Wolff representation
Vladimir Belitsky (IME/USP) – Uniqueness of Gibbs state for non-ideal gas in Rd: the case of multi-body interaction
Alexander Elgart (Princeton University) – Adiabatic theorem and Kubo formula for dense point spectrum
Silvio Renato Dahmen (Univ.Fed.Rio G. do Sul) – Directed percolation and the Lee-Yang theory
Hirofumi Osada (Nagoya Univ.) – Interacting brownian motions with logarithmic potentials
Narn-Rueih Shieh (Nat. Taiwan Univ.) – Multifractals on Galton-Watson trees
Hermann Shulz-Baldes (Univ. Cal., Irvine) – Delocalization for one-dimensional Random operators
Marton Balazs (Inst. Math. TU, Budapest) – Structure of the shock in a new domain growth model
Alexandre Baraviera  (IMPA) – Robust non uniform hyperbolicity for volume preserving maps
Mauricio D. Coutinho-Filho (Univ.Fed. Pernambuco) – Field theory and statistical mechanics of quantum ferromagnetic Spin chains
Aniura Barrientos (IMPA) – Some results about a bidimensional version of the generalized BO
Yoo, Hyun Jae (Tokyo Inst. of Tech.) – Fermion Random point fields as Gibbs measures and an application
Robert Sims (Univ. of Alabama, Birmingham) – Fractional moment methods for finite rank perturbations
Michael Landrigan (Univ. of Cal. Irvine) – Log continuity for Sturmian Hamiltonians
Jung Ming Woo (Univ. of Southern Cal.) – A Gaussian behaviour of Random conductivities on hierarchical lattices
Firas Rassoul-Agha (Courant Inst. NYU) – Rwre: particle story
Dirk Hundertmark (CALTECH)  – A diamagnetic inequality for semigroup differences
Fulvio Baldovin (CBPF) – Nonstandard mixing in the standard map
Rémy Sanchis (Univ. Fed. Minas Gerais) – Analycity of the d-dimensional bond percolation probability around  p – 1
Laurent Miclo (Univ. Paul Sabatier) – On  projection of  logaritmic Sobolev inequalities
Andrei Toom (Univ. Fed. Pernambuco) – On critical values for some Random processes with local interaction in a plane
Beat Niederhauser (IME/USP) – Phase transition in the Hopfield Model with p-Spin interactions

 

Participants

M. Aizenman Princeton Univ.
M. Balazs Technical Univ., Budapest
F. Baldovin CBPF
A.T. Baraviera IMPA
A.M. Barrientos IMPA
V. Belitsky IME/USP
J. Bertoin Université Paris VI
J. Bourgain Princeton IAS
F. Camia Courant Institute
M. Campbell Univ. California, Irvine
F. Castellares USP, Brasil
R. Cerf Univ. Paris XI
E.G.D. Cohen Rockefeller
J-M. Combes Univ. Toulon
M.D. Coutinho-Filho UFPE
G.A.Torres F. da Costa UFSC
P.A. Faria da Veiga USP, Brasil
S.R. Dahmen UFRGS
D. T. Damanik Caltech, USA
E. de Faria USP
B. N. Borges de Lima IMPA, Brasil
W. de Melo IMPA, Brasil
C. R. de Oliveira UFScar, Brasil
B. Duplantier SPhT, CEA Saclay
A. Elgart Princeton Univ., USA
A. Figotin Univ. Of California, Irvine, USA
M. V. Freire USP, Brasil
F. Germinet Univ. Lille I
F. Guerra Univ. Roma I
T. Hara Nagoya University
H. Hermmann ESPCI Paris
P. Hislop Kentucky Univ.
D. Hundertmark Caltech, USA
S. Jitomirskaya UC – Irvine
J.-H. Kim Yonsei Univ.
W. Kirsch Bochum Univ.
A. Klein UC – Irvine
F. Klopp Univ. Paris XIII
A. Kupiainen Univ. Helsinki
M.D. Landrigan Univ. California, USA
G. Lawler Duke University
Y. Le Jan Univ. Paris XI
D.H.U. Marchetti IF/USP
L. Miclos Univ. Paul Sabatier
B.M. Niederhauser USP, Brasil
G. M. Noronha Neto IMPA, Brasil
M.L. O’Carroll UFMG, Brasil
H. Osada Nagoya University
J. Palis IMPA, Brasil
A. Pisztora Carnegie-Mellon
E. Presutti Univ. Roma II
A.F. Ramirez PUC/Chile
J. Ramirez Cornell University
F. Rassoul-Agha Courant Institute
T. L. Rotchie USP, Brasil
L.T. Rolla UFMG, Brasil
Y. Saint-Aubin Montreal Univ.
R. de Paiva Sanchiz UFMG, Brasil
H. Schulz-Baldes Univ. California, Irvine
N.R. Shieh National Univ. of Taiwan
V. Sidoravicius IMPA, Brasil
R. Sims PUC/Chile
S. Smirnov KTH
G. Stolz Alabama Univ.
Y. Suhov Cambridge, UK
F.L. Toninelli PUC/Chile
A. Toom UFPE
C. Tsallis CBPF, Brasil
G. Valle da Silva Coelho PUC/Chile
M.E. Vares IMPA
G.L. Vasconcelos UFPE
W.-M. Wang Univ. Paris XI
J. Wierman J.Hopkins Univ.
J.M. Woo Univ. Southern California, USA
J.-C. Yoccoz Collége de France
H.J. Yoo Tokyo Inst. Technology

 

 

Registration Fee

Students
R$ 30,00
Others (due upon arrival at the Conference)
U$ 50.00

 

Accomodations

The Workshop on Mathematical Physics will take place at the Hotel do Bosque in Mambucaba, Rio de Janeiro.

 

Department of Scientific Activities

dac@impa.br
IMPA, Estrada Dona Castorina 110
22460-320 Rio de Janeiro, Brazil
Fax: +55 (21) 529-5019