15 research outputs found
A stronger topology for the Brownian web
We propose a metric space of coalescing pairs of paths on which we are able
to prove (more or less) directly convergence of objects such as the persistence
probability in the (one dimensional, nearest neighbor, symmetric) voter model
or the diffusively rescaled weight distribution in a silo model (as well as the
equivalent output distribution in a river basin model), interpreted in terms of
(dual) diffusively rescaled coalescing random walks, to corresponding objects
defined in terms of the Brownian web.Comment: 22 page
Repulsion of an evolving surface on walls with random heights
We consider the motion of a discrete random surface interacting by exclusion with a random wall. The heights of the wall at the sites of Z(d) are i.i.d. random variables. Fixed the wall configuration, the dynamics is given by the serial harness process which is not allowed to go below the wall. We study the effect of the distribution of the wall heights on the repulsion speed. (c) 2005 Elsevier SAS. All rights reserved.42220721
Dynamic phase diagram of the REM
By studying the two-time overlap correlation function, we give a
comprehensive analysis of the phase diagram of the Random Hopping Dynamics of
the Random Energy Model (REM) on time-scales that are exponential in the
volume. These results are derived from the convergence properties of the clock
process associated to the dynamics and fine properties of the simple random
walk in the -dimensional discrete cube.Comment: This paper is in large part based on the unpublished work
arXiv:1008.3849. In particular, the analysis of the overlap correlation
function is new as well as the study of the high temperature and short
time-scale transition line between aging and stationarit
Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman
In the introduction to this volume, we discuss some of the highlights of the
research career of Chuck Newman. This introduction is divided into two main
sections, the first covering Chuck's work in statistical mechanics and the
second his work in percolation theory, continuum scaling limits, and related
topics.Comment: 38 pages (including many references), introduction to Festschrift in
honor of C.M. Newma
Guidelines for the use and interpretation of assays for monitoring autophagy (4th edition)1.
In 2008, we published the first set of guidelines for standardizing research in autophagy. Since then, this topic has received increasing attention, and many scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Thus, it is important to formulate on a regular basis updated guidelines for monitoring autophagy in different organisms. Despite numerous reviews, there continues to be confusion regarding acceptable methods to evaluate autophagy, especially in multicellular eukaryotes. Here, we present a set of guidelines for investigators to select and interpret methods to examine autophagy and related processes, and for reviewers to provide realistic and reasonable critiques of reports that are focused on these processes. These guidelines are not meant to be a dogmatic set of rules, because the appropriateness of any assay largely depends on the question being asked and the system being used. Moreover, no individual assay is perfect for every situation, calling for the use of multiple techniques to properly monitor autophagy in each experimental setting. Finally, several core components of the autophagy machinery have been implicated in distinct autophagic processes (canonical and noncanonical autophagy), implying that genetic approaches to block autophagy should rely on targeting two or more autophagy-related genes that ideally participate in distinct steps of the pathway. Along similar lines, because multiple proteins involved in autophagy also regulate other cellular pathways including apoptosis, not all of them can be used as a specific marker for bona fide autophagic responses. Here, we critically discuss current methods of assessing autophagy and the information they can, or cannot, provide. Our ultimate goal is to encourage intellectual and technical innovation in the field
Time fluctuations of the random average process with parabolic initial conditions
The random average process is a randomly evolving d-dimensional surface whose heights are updated by random convex combinations of neighboring heights. The fluctuations of this process in case of linear initial conditions have been studied before. In this paper, we analyze the case of polynomial initial conditions of degree 2 and higher. Specifically, we prove that the time fluctuations of a initial parabolic surface are of order n(2-d/2) for d=1,2,3; log n in d=4; and are bounded in d greater than or equal to 5. We establish a central limit theorem in d = 1. In the bounded case of d greater than or equal to 5, we exhibit an invariant measure for the process as seen from the average height at the origin and describe its asymptotic space fluctuations. We consider briefly the case of initial polynomial surfaces of higher degree to show that their time fluctuations are not bounded in high dimensions, in contrast with the linear and parabolic cases. (C) 2002 Elsevier Science B.V. All rights reserved.103225727