42 research outputs found
Front progression for the East model
The East model is a one-dimensional, non-attractive interacting particle
system with Glauber dynamics, in which a flip is prohibited at a site if
the right neighbour is occupied. Starting from a configuration entirely
occupied on the left half-line, we prove a law of large numbers for the
position of the left-most zero (the front), as well as ergodicity of the
process seen from the front. For want of attractiveness, the one-dimensional
shape theorem is not derived by the usual coupling arguments, but instead by
quantifying the local relaxation to the non-equilibrium invariant measure for
the process seen from the front. This is the first proof of a shape theorem for
a kinetically constrained spin model.Comment: 38 pages, 9 figures; typos corrected and some details added since the
first versio
Tracer diffusion at low temperature in kinetically constrained models
We describe the motion of a tracer in an environment given by a kinetically
constrained spin model (KCSM) at equilibrium. We check convergence of its
trajectory properly rescaled to a Brownian motion and positivity of the
diffusion coefficient as soon as the spectral gap of the environment is
positive (which coincides with the ergodicity region under general conditions).
Then we study the asymptotic behavior of when the density of the
environment goes to in two classes of KCSM. For noncooperative models, the
diffusion coefficient scales like a power of , with an exponent that we
compute explicitly. In the case of the Fredrickson-Andersen one-spin
facilitated model, this proves a prediction made in Jung, Garrahan and Chandler
[Phys. Rev. E 69 (2004) 061205]. For the East model, instead we prove that the
diffusion coefficient is comparable to the spectral gap, which goes to zero
faster than any power of . This result contradicts the prediction of
physicists (Jung, Garrahan and Chandler [Phys. Rev. E 69 (2004) 061205; J.
Chem. Phys. 123 (2005) 084509]), based on numerical simulations, that suggested
with .Comment: Published at http://dx.doi.org/10.1214/14-AAP1017 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A class of random walks in reversible dynamic environment: antisymmetry and applications to the East model
We introduce via perturbation a class of random walks in reversible dynamic
environments having a spectral gap. In this setting one can apply the
mathematical results derived in http://arxiv.org/abs/1602.06322. As first
results, we show that the asymptotic velocity is antisymmetric in the
perturbative parameter and, for a subclass of random walks, we characterize the
velocity and a stationary distribution of the environment seen from the walker
as suitable series in the perturbative parameter. We then consider as a special
case a random walk on the East model that tends to follow dynamical interfaces
between empty and occupied regions. We study the asymptotic velocity and
density profile for the environment seen from the walker. In particular, we
determine the sign of the velocity when the density of the underlying East
process is not 1/2, and we discuss the appearance of a drift in the balanced
setting given by density 1/2
Random walk on random walks: low densities
We consider a random walker in a dynamic random environment given by a system
of independent simple symmetric random walks. We obtain ballisticity results
under two types of perturbations: low particle density, and strong local drift
on particles. Surprisingly, the random walker may behave very differently
depending on whether the underlying environment particles perform lazy or
non-lazy random walks, which is related to a notion of permeability of the
system. We also provide a strong law of large numbers, a functional central
limit theorem and large deviation bounds under an ellipticity condition.Comment: 28 page
Recommended from our members
Random walk on random walks: Low densities
We consider a random walker in a dynamic random environment given by a
system of independent simple symmetric random walks. We obtain ballisticity
results under two types of perturbations: low particle density, and strong
local drift on particles. Surprisingly, the random walker may behave very
differently depending on whether the underlying environment particles perform
lazy or non-lazy random walks, which is related to a notion of permeability
of the system. We also provide a strong law of large numbers, a functional
central limit theorem and large deviation bounds under an ellipticity
condition
Random walk on random walks: Higher dimensions
We study the evolution of a random walker on a conservative dynamic
random environment composed of independent particles performing simple
symmetric random walks, generalizing results of [16] to higher dimensions and
more general transition kernels without the assumption of uniform ellipticity
or nearest-neighbour jumps. Specifically, we obtain a strong law of large
numbers, a functional central limit theorem and large deviation estimates for
the position of the random walker under the annealed law in a high density
regime. The main obstacle is the intrinsic lack of monotonicity in
higher-dimensional, non-nearest neighbour settings. Here we develop more
general renormalization and renewal schemes that allow us to overcome this
issue. As a second application of our methods, we provide an alternative
proof of the ballistic behaviour of the front of (the discrete-time version
of) the infection model introduced in [23]
Hydrodynamic limit for a facilitated exclusion process
International audienceWe study the hydrodynamic limit for a periodic 1-dimensional exclusion process with a dynamical constraint, which prevents a particle at site x from jumping to site x ± 1 unless site x 1 is occupied. This process with degenerate jump rates admits transient states, which it eventually leaves to reach an ergodic component, assuming that the initial macroscopic density is larger than 1 2 , or one of its absorbing states if this is not the case. It belongs to the class of conserved lattice gases (CLG) which have been introduced in the physics literature as systems with active-absorbing phase transition in the presence of a conserved field. We show that, for initial profiles smooth enough and uniformly larger than the critical density 1 2 , the macroscopic density profile for our dynamics evolves under the diffusive time scaling according to a fast diffusion equation (FDE). The first step in the proof is to show that the system typically reaches an ergodic component in subdiffusive time.Nous Ă©tudions la limite hydrodynamique d'un systĂšme d'exclusion unidimensionnel avec une contrainte dynamique, qui empĂȘche une particule en x de sauter en x ± 1 Ă moins que x â 1 soit occupĂ©. Ce processus Ă taux de sauts dĂ©gĂ©nĂ©rĂ©s admet des Ă©tats transients, qu'il finit par quitter pour atteindre une composante ergodique dans le cas oĂč la densitĂ© initiale macroscopique est supĂ©rieure Ă 1 2 , ou un de ses Ă©tats absorbants dans l'autre cas. Ce processus fait partie des gaz conservatifs sur rĂ©seau, qui ont Ă©tĂ© introduits dans la litĂ©rature physique comme systĂšmes prĂ©sentant une transition de phase active-absorbante en prĂ©sence d'un champ conservĂ©. Nous montrons que pour des profils initiaux de densitĂ© suffisamment rĂ©guliers et strictement supĂ©rieurs Ă 1 2 , le profil de densitĂ© macroscopique Ă©volue Ă l'Ă©chelle diffusive suivant une Ă©quation de diffusion rapide (FDE). La premiĂšre Ă©tape de la preuve consiste Ă montrer que, typiquement, le systĂšme atteint une composante ergodique en temps sous-diffusif
Dynamics of interacting particle systems******
We collect here recent results covering various aspects of the dynamical properties of interacting particle systems. In Section 1 we study the hydrodynamic limit of a facilitated exclusion process. Section 2 evidences a cutoff phenomenon for the mixing time of the weakly asymmetric exclusion process. Section 3 presents a study of the infection time in the Duarte model. Finally, Section 4 presents the study of a front propagation in the FA-If model
COVID-19 symptoms at hospital admission vary with age and sex: results from the ISARIC prospective multinational observational study
Background:
The ISARIC prospective multinational observational study is the largest cohort of hospitalized patients with COVID-19. We present relationships of age, sex, and nationality to presenting symptoms.
Methods:
International, prospective observational study of 60â109 hospitalized symptomatic patients with laboratory-confirmed COVID-19 recruited from 43 countries between 30 January and 3 August 2020. Logistic regression was performed to evaluate relationships of age and sex to published COVID-19 case definitions and the most commonly reported symptoms.
Results:
âTypicalâ symptoms of fever (69%), cough (68%) and shortness of breath (66%) were the most commonly reported. 92% of patients experienced at least one of these. Prevalence of typical symptoms was greatest in 30- to 60-year-olds (respectively 80, 79, 69%; at least one 95%). They were reported less frequently in children (â€â18 years: 69, 48, 23; 85%), older adults (â„â70 years: 61, 62, 65; 90%), and women (66, 66, 64; 90%; vs. men 71, 70, 67; 93%, each Pâ<â0.001). The most common atypical presentations under 60 years of age were nausea and vomiting and abdominal pain, and over 60 years was confusion. Regression models showed significant differences in symptoms with sex, age and country.
Interpretation:
This international collaboration has allowed us to report reliable symptom data from the largest cohort of patients admitted to hospital with COVID-19. Adults over 60 and children admitted to hospital with COVID-19 are less likely to present with typical symptoms. Nausea and vomiting are common atypical presentations under 30 years. Confusion is a frequent atypical presentation of COVID-19 in adults over 60 years. Women are less likely to experience typical symptoms than men