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Secondorder fluctuations and current across characteristic for a onedimensional growth model of independent random
, 2005
"... Fluctuations from a hydrodynamic limit of a onedimensional asymmetric system come at two levels. On the central limit scale n 1/2 one sees initial fluctuations transported along characteristics and no dynamical noise. The second order of fluctuations comes from the particle current across the chara ..."
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Cited by 14 (2 self)
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Fluctuations from a hydrodynamic limit of a onedimensional asymmetric system come at two levels. On the central limit scale n 1/2 one sees initial fluctuations transported along characteristics and no dynamical noise. The second order of fluctuations comes from the particle current across the characteristic. For a system made up of independent random walks we show that the secondorder fluctuations appear at scale n 1/4 and converge to a certain selfsimilar Gaussian process. If the system is in equilibrium, this limiting process specializes to fractional Brownian motion with Hurst parameter 1/4. This contrasts with asymmetric exclusion and Hammersley’s process whose secondorder fluctuations appear at scale n 1/3, as has been discovered through related combinatorial growth models. 1. Introduction. An
The Random Average Process and Random Walk in a SpaceTime Random Environment in One Dimension
 MATHEMATICAL PHYSICS
, 2006
"... We study spacetime fluctuations around a characteristic line for a onedimensional interacting system known as the random average process. The state of this system is a realvalued function on the integers. New values of the function are created by averaging previous values with random weights. Th ..."
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Cited by 11 (4 self)
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We study spacetime fluctuations around a characteristic line for a onedimensional interacting system known as the random average process. The state of this system is a realvalued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n 1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known productform invariant distributions, this limit is a twoparameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a spacetime random environment. These limits also happen at scale n 1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.
Directed random growth models on the plane
, 2008
"... This is a brief survey of laws of large numbers, fluctuation results and large deviation principles for asymmetric interacting particle systems that represent moving interfaces on the plane. We discuss the exclusion process, the Hammersley process and the related lastpassage growth models. ..."
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Cited by 2 (0 self)
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This is a brief survey of laws of large numbers, fluctuation results and large deviation principles for asymmetric interacting particle systems that represent moving interfaces on the plane. We discuss the exclusion process, the Hammersley process and the related lastpassage growth models.
Contents PART I Preliminaries 4
, 2008
"... 1.1 Discretetime Markov chains........................... 4 1.2 Continuoustime Markov chains......................... 6 ..."
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1.1 Discretetime Markov chains........................... 4 1.2 Continuoustime Markov chains......................... 6
H E U
, 2011
"... Over the last few decades the interests of statistical physicists have broadened to include the detailed quantitative study of many systems – chemical, biological and even social – that were not traditionally part of the discipline. These systems can feature rich and complex spatiotemporal behaviour ..."
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Over the last few decades the interests of statistical physicists have broadened to include the detailed quantitative study of many systems – chemical, biological and even social – that were not traditionally part of the discipline. These systems can feature rich and complex spatiotemporal behaviour, often due to continued interaction with the environment and characterised by the dissipation of flows of energy and/or mass. This has led to vigorous research aimed at extending the established theoretical framework and adapting analytical methods that originate in the study of systems at thermodynamic equilibrium to deal with outofequilibrium situations, which are much more prevalent in nature. This thesis focuses on a microscopic model known as the asymmetric exclusion process, or ASEP, which describes the stochastic motion of particles on a onedimensional lattice. Though in the first instance a model of a lattice gas, it is sufficiently general to have served as the basis to model a wide variety of phenomena. That, as well as substantial progress made in analysing its stationary behaviour, including the locations and nature