» Program:
(Tentatively, one full hour should also include a 5-10 minutes discussing time)
| Monday, June
27 |
Tuesday,
June 28 |
Wednesday,
June 29 |
Thursday,
June 30 |
Friday, July
1 |
Saturday,
July 2 |
|
| 9.00
- 10.00 |
Guerra | Aizenman | Guerra | Newman |
Stein |
Talagrand |
| 10.00 - 11.00 | Aizenman | Guerra |
Aizenman | Stein |
Talagrand |
Nishimori |
| 11.00 - 11.30 |
coffee break | coffee break | coffee break | coffee break | coffee break | coffee break |
| 11.30 - 12.30 |
Derrida | Parisi |
Newman | Talagrand |
Ben Arous |
Bovier |
| 12.30 - 14.30 |
lunch |
lunch | lunch | lunch | lunch | lunch |
| 14.30 - 15.30 |
Olivieri |
Franz | Giardinà | Guionnet | De Sanctis | |
| 15.30 - 16.30 |
Contucci |
Marinari |
Toninelli | Isopi |
||
| 16.30 - 17.00 |
coffee break | coffee break | coffee break | coffee break | ||
| 17.00 - 18.00 |
Shcherbina | Fröhlich | Lebowitz | Panchenko |
On Wednesday, June 29, from 6.15 to 7 pm Joel Lebowitz will chair an Informal Session on Human Rights
Lectures:
Michael Aizenman
Title:
Abstract:
Francesco Guerra
Title:
Overlap locking in mean field spin glasses
Abstract:
In the frame of interpolation methods, we show how comparison
systems are able
to lock their overlaps to those of a mean field spin glass.
Locking power is expressed in terms of overlap fluctuations. We give as examples the case
of the annealed approximation, the replica
symmetric approximation, and the Parisi representation. A
byproduct of our treatment
is a simple proof that replica symmetry holds up to the Almeida-Thouless line.
Chuck Newman & Dan Stein
Title:
Short-Range Spin Glasses
Abstract:
We review results about
short-range spin glasses at low and zero temperature. We will
focus on
what is presently known, and what we believe might be provable
in the near future. Our focus is on low-temperature
equilibrium properties of short-range spin glasses, including: numbers
of pure
and ground states in various dimensions;
the nature of excitations and
interfaces and their connection to pure state structure; the use of
metastates to analyze
the organization of the broken-symmetric structure of the
low-temperature phase.
Michel Talagrand
Title:
Large Deviations, Guerra and A.S.S. schemes and the Parisi
hypothesis
Abstract:
We consider the problem of computing$$
\lim_{N \rightarrow \infty} \frac{1}{Na} E \log Z_N $$when
$a$ is a real number and $Z_N$ is the partition function of theSK
model. We review in this setting some of the recent ideas that seemfruitful.
Gerard Ben Arous
Title:
The Arcsine law for stable subordinators as a universal mechanism of
Aging for spinglass dynamics?
Abstract:
Anton Bovier
Title:
The local REM conjcture and beyond
Abstract:
Recently, Bauke and Mertens conjectured that the local statistics of energies in
random spin systems with discretespin space should in most circumstances be the same as in
the randomenergy model. Here we
give necessary
conditions for this hypothesis to be true, which we
show to hold in wide classes of examples: shortrange
spin
glasses and mean field spin glasses of the SK type. We alsoshow
that, under certain conditions, the conjecture holds even if energy levels that grow moderatelywith
the volume of the system are considered. Finally,
we show that the conjecture
fails if levels near the extremes are
considered, and show that a complex and rich structure emerges inthiscase
in the
example of Derrida's generalized random energy models.
Pierluigi Contucci
Title:
The Ghirlanda-Guerra Identities
Abstract:
We will show a proof of the Ghirlanda-Guerra identities which only requires that the
variance of the Hamiltonian grows
like the volume (thermodynamic stability). Our result is expressed in terms
of the model's covariance and
applies to all known spin glass models.
Bernard Derrida
Title:
Noisy traveling waves in evolution models and spin glasses
Abstract:
Models of evolution in presence of selection can be formulated as noisy traveling waves. This
talk will review
some recent results obtained on the effect of noise on the velocity and
of the diffusion constant of these noisy
traveling waves. The
exact solution of a special case reveals statistical properties of
trees which are
quantitatively identical to those of spin glasses, as predicted by the Parisi
broken symmetry of replica.
Luca De Sanctis
Title:
Overlap Structure approach to various spin glass models
Abstract:
We show how Random (Multi-)
Overlap Structures can be used to approach various spin glass models,
in particular
diluted systems and optimization problems.
We illustrate some advantages and disadvantages of possible
Ansatzs
that can be formulated in such context
Silvio Franz
Title:
A field-theoretical approach to the spin glass transition
Abstract:
We study spin glasses with Kac type interaction potential for small but
finite inverse interaction range $\gamma$. Using the
theoretical setup
of
coupled replicas, through the replica method we argue that the
probability of
overlap profiles can be
expressed for small $\gamma$ through a
large-deviation
functional. This result is supported by rigorous arguments, showing
that the
large-deviation functional provides at least upper bounds for the
probability.
Finally we analyze the rate function, in the
vicinity of the critical
point
$T_c=1$ of mean field theory, and we study the free energy cost of
overlap
interfaces, assuming the
validity of a gradient expansion for the rate
functional.
Jürg Fröhlich
Title:
Abstract:
Cristian Giardina'
Title:
On the (link) overlap distribution on the Edwards-Anderson model.
Abstract:
In the first part of the talk, we will give a rigorous formulation of the Stochastic
Stability property for a large
class of Gaussian spin
glass models. From this we will
obtain some well-known identities among overlaps moments, which are included
in the Ghirlanda-Guerra
identities. Then we specialize to Edward-Anderson model for which we present a
numerical study of the overlap factorization
properties.
Alice Guionnet
Title:
Dynamics for spherical SK dynamics
Abstract:
We consider the Langevin dynamics for p-spins model of
Sherrington-Kirkpatrick model.
We prove convergence of the empirical distribution of
the particles. The limit is
described by a coupled integro-differential system involving the dynamical
covariance and the
response function.
We discuss the long time
asymptotics of the solution in
the high temperature regime and the FDT regime, following works of
Cugliandolo,
Kurchan et al.
Marco Isopi
Title:
Coarsening on a one-dimensional lattice: the continuum limit
Abstract:
Coarsening on a one-dimensional lattice is described by the voter
model or equivalently by coalescing (or annihilating)
random walks
representing the evolving boundaries between regions of constant
color and by backward (in time)
coalescing random walks
corresponding to color genealogies.
Asympotics for large time and space on the lattice are
described via a continuum space-time voter model whose boundary motion
is expressed by the Brownian web (BW) of coalescing
forward Brownian motions.
I will describe how small noise in the voter model, corresponding to
the nucleation of
randomly
colored regions, can be treated in the continuum limit.
Joel Lebowitz
Title:
Fluctuations, Large Deviations, and the Custom Construction of Point Processes
Abstract:
I will review some aspects of fluctuations in equilibrium and nonequilibrium systems with
emphasis on their relation to large
deviations and entropy. I will then describe some recent work on the construction of point
processes with specified low order correlations.
These specify, among other things, the variance of the
fluctuations of local
quantities.
Enzo Marinari
Title:
Low T scaling behavior of 2D disordered and frustrated models.
Abstract:
The ground state and low T behavior of two-dimensional spin
systems with discrete
binary couplings are subtle. I present an analysis based
on exact computations of finite volume partition functions. I
first discuss the fully
frustrated model without disorder, and then introduce
disorder by changing random links (spin glass) or by unfrustrating random
plaquettes (plaquette disorder). In both cases
the introduction of disorder changes the properties of the T=0 critical point.
Hidetoshi Nishimori
Title:
Duality in spin glasses
Abstract:
I prove the existence of duality relations in finite-dimensional spin glass models under
replica formalism.
The models are shown to be self-dual under certain conditions. Assuming analyticity of
duality transformation, I derive
relations between
transition points, which determine the critical point if it is unique. If one
accepts the zero-replica limit
as a legitimate replacement
of average over quenched randomness, our method gives the (possibly exact)
location
of the multicritical point in the
phase diagram of quenched system. The results are in impressive agreement with
numerical investigations in all available cases.
Enzo Olivieri
Title:
Disordered systems close to criticality.
Abstract:
We consider disordered lattice spin systems. In particular we
analyze small random
perturbations of strong mixing systems
giving rise to the
Griffiths' phase. We use
a graded cluster expansion with a minimal length depending on the thermodynamic
parameters. On the lowest
length scale, contrary to the usual high temperature or large magnetic field
perturbative theories
we use a "scale-adapted cluster expansion
" based on a suitable finite size mixing condition. We rely on a general theory
already applied to the problem of proving weak Gibbsianity and convergence of the iterates for a class of
renormalization
group maps.
Dmitry Panchenko
Title:
On the generalized Sherrington-Kirkpatrick model.
Abstract:
I will present the extension of the Talagrand's proof of the Parisi
formula to a general class of the SK-type models with spins
distributed according to an arbitrary probability measure on a bounded
subset of
the real line. I will describe the analogue
of the Parisi formula,
the replica symmetric region and talk about some properties of the
Parisi functional.
Giorgio Parisi
Title:
The art of computing complexity
Abstract:
In this talk I will review some of the recent results in
computing the exponentially
large nmber of metastable states (often identified with
the solutions of the TAP equations) in the infinite range limit
(SK model) for spin
glasses and on the Bethe lattice.
top
Mariya Shcherbina
Title:
Cavity methods in the dynamics of neurons systems
Abstract:
The dynamics of systems of $N$ neurons governed by the system of liner or
nonlinear differential equations
with random
coefficients will be discussed. The
statistical distribution (as $N\to\infty$) of neurons on the real line at any fixed time $t$
is studied using the cavity method.
Fabio Lucio Toninelli
Title:
Random copolymers at a selective interface: phase diagram
and some path
properties
Abstract:
I will consider a model of a random heterogeneous polymer in the proximity
of an interface separating two
selective solvents. This model exhibits a localization/delocalization
transition. A positive value of
the free
energy corresponds to the localized regime and strong results on the polymer path behavior are
known in
this case. I will focus on the interior of the delocalized phase, which
is characterized by the free energy equal to zero,
and I will show in particular that in this regime there are
O(log N) monomers in the
unfavorable solvent
(N is the length of the polymer). The previously known result was o(N). Another
result concerns the weak coupling
limit: we show the
universal nature of this limit, previously considered only for binary disorder. Although the
physics of the model is quite far from that of spin glasses, I will show
that the mathematical tools which
are essential in the solution of the SK model (i.e.,
interpolation and concentration
of measure) play an essential
role also in this case.