960 research outputs found
A (2+1)-dimensional growth process with explicit stationary measures
We introduce a class of (2+1)-dimensional stochastic growth processes, that
can be seen as irreversible random dynamics of discrete interfaces.
"Irreversible" means that the interface has an average non-zero drift.
Interface configurations correspond to height functions of dimer coverings of
the infinite hexagonal or square lattice. The model can also be viewed as an
interacting driven particle system and in the totally asymmetric case the
dynamics corresponds to an infinite collection of mutually interacting
Hammersley processes.
When the dynamical asymmetry parameter equals zero, the
infinite-volume Gibbs measures (with given slope ) are
stationary and reversible. When , are not reversible any
more but, remarkably, they are still stationary. In such stationary states, we
find that the average height function at any given point grows linearly
with time with a non-zero speed: while the typical fluctuations of are
smaller than any power of as .
In the totally asymmetric case of and on the hexagonal lattice, the
dynamics coincides with the "anisotropic KPZ growth model" introduced by A.
Borodin and P. L. Ferrari. For a suitably chosen, "integrable", initial
condition (that is very far from the stationary state), they were able to
determine the hydrodynamic limit and a CLT for interface fluctuations on scale
, exploiting the fact that in that case certain space-time
height correlations can be computed exactly.Comment: 37 pages, 13 figures. v3: some references added, introduction
expanded, minor changes in the bul
Disordered pinning models and copolymers: beyond annealed bounds
We consider a general model of a disordered copolymer with adsorption. This
includes, as particular cases, a generalization of the copolymer at a selective
interface introduced by Garel et al. [Europhys. Lett. 8 (1989) 9--13], pinning
and wetting models in various dimensions, and the Poland--Scheraga model of DNA
denaturation. We prove a new variational upper bound for the free energy via an
estimation of noninteger moments of the partition function. As an application,
we show that for strong disorder the quenched critical point differs from the
annealed one, for example, if the disorder distribution is Gaussian. In
particular, for pinning models with loop exponent this implies
the existence of a transition from weak to strong disorder. For the copolymer
model, under a (restrictive) condition on the law of the underlying renewal, we
show that the critical point coincides with the one predicted via
renormalization group arguments in the theoretical physics literature. A
stronger result holds for a "reduced wetting model" introduced by Bodineau and
Giacomin [J. Statist. Phys. 117 (2004) 801--818]: without restrictions on the
law of the underlying renewal, the critical point coincides with the
corresponding renormalization group prediction.Comment: Published in at http://dx.doi.org/10.1214/07-AAP496 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Spiral model, jamming percolation and glass-jamming transitions
The Spiral Model (SM) corresponds to a new class of kinetically constrained
models introduced in joint works with D.S. Fisher [8,9]. They provide the first
example of finite dimensional models with an ideal glass-jamming transition.
This is due to an underlying jamming percolation transition which has
unconventional features: it is discontinuous (i.e. the percolating cluster is
compact at the transition) and the typical size of the clusters diverges faster
than any power law, leading to a Vogel-Fulcher-like divergence of the
relaxation time. Here we present a detailed physical analysis of SM, see [5]
for rigorous proofs. We also show that our arguments for SM does not need any
modification contrary to recent claims of Jeng and Schwarz [10].Comment: 9 pages, 7 figures, proceedings for StatPhys2
Kinetically constrained spin models on trees
We analyze kinetically constrained 0-1 spin models (KCSM) on rooted and
unrooted trees of finite connectivity. We focus in particular on the class of
Friedrickson-Andersen models FA-jf and on an oriented version of them. These
tree models are particularly relevant in physics literature since some of them
undergo an ergodicity breaking transition with the mixed first-second order
character of the glass transition. Here we first identify the ergodicity regime
and prove that the critical density for FA-jf and OFA-jf models coincide with
that of a suitable bootstrap percolation model. Next we prove for the first
time positivity of the spectral gap in the whole ergodic regime via a novel
argument based on martingales ideas. Finally, we discuss how this new technique
can be generalized to analyze KCSM on the regular lattice .Comment: Published in at http://dx.doi.org/10.1214/12-AAP891 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Dynamical arrest, tracer diffusion and Kinetically Constrained Lattice Gases
We analyze the tagged particle diffusion for kinetically constrained models
for glassy systems. We present a method, focusing on the Kob-Andersen model as
an example, which allows to prove lower and upper bounds for the self diffusion
coefficient . This method leads to the exact density dependence of
, at high density, for models with finite defects and to prove
diffusivity, , at any finite density for highly cooperative models. A
more general outcome is that under very general assumptions one can exclude
that a dynamical transition, like the one predicted by the Mode-Coupling-Theory
of glasses, takes place at a finite temperature/chemical potential for systems
of interacting particles on a lattice.Comment: 28 pages, 4 figure
The Atlantic divide: methodological and epistemological differences in economic history
In the paper the development of economic history will be placed within the evolution of Western thought and culture. Therefore an analysis of the connections between economic history and contemporary epistemology will be carried out. In this perspective an analogy with the traditional division between analytic philosophy and continental philosophy would appear to be useful for economic history too: the first had long prevailed in Anglo-Saxon, the second in continental, culture. This partition evokes and embraces the antithesis between scientific and humanist culture, between logic and rhetoric, analysis and interpretation, conceptual clarification and visions of the world. The paper suggest that the opposition that loomed large over the post W.W.II decades between Anglo-American and European economic histories can also be conceived as a specific form of the wider opposition between âanalytic styleâ and âcontinental styleâ.economic history, methodology, epistemology, cliometrics, business history, economic thought
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