TAILIEUCHUNG - Đề tài " (log t)2/3 law of the two dimensional asymmetric simple exclusion process "

We prove that the diffusion coefficient for the two dimensional asymmetric simple exclusion process with nearest-neighbor-jumps diverges as (log t)2/3 to the leading order. The method applies to nearest and non-nearest neighbor asymmetric simple exclusion processes. 1. Introduction The asymmetric simple exclusion process is a Markov process on {0, 1}Z with asymmetric jump rates. There is at most one particle allowed per site and thus the word exclusion. The particle at a site x waits for an exponential time and then jumps to y with rate p(x − y) provided that the site is not occupied. . | Annals of Mathematics log t 2 3 law of the two dimensional asymmetric simple exclusion process By Horng-Tzer Yau Annals of Mathematics 159 2004 377 405 log t 2 3 law of the two dimensional asymmetric simple exclusion process By Horng-Tzer Yau Abstract We prove that the diffusion coefficient for the two dimensional asymmetric simple exclusion process with nearest-neighbor-jumps diverges as logt 2 3 to the leading order. The method applies to nearest and non-nearest neighbor asymmetric simple exclusion processes. 1. Introduction The asymmetric simple exclusion process is a Markov process on 0 1 Zd with asymmetric jump rates. There is at most one particle allowed per site and thus the word exclusion. The particle at a site x waits for an exponential time and then jumps to y with rate p x y provided that the site is not occupied. Otherwise the jump is suppressed and the process starts again. The jump rate is assumed to be asymmetric so that in general there is net drift of the system. The simplicity of the model has made it the default stochastic model for transport phenomena. Furthermore it is also a basic component for models 5 12 with incompressible Navier-Stokes equations as the hydrodynamical equation. The hydrodynamical limit of the asymmetric simple exclusion process was proved by Rezakhanlou 13 to be a viscousless Burgers equation in the Euler scaling limit. If the system is in equilibrium the Burgers equation is trivial and the system moves with a uniform velocity. This uniform velocity can be removed and the viscosity of the system or the diffusion coefficient can be defined via the standard mean square displacement. Although the diffusion coefficient is expected to be finite for dimension d 2 a rigorous proof was obtained only a few years ago 9 by estimating the corresponding resolvent equation. Based on the mode coupling theory Beijeren Kutner and Spohn 3 Work partially supported by NSF grant DMS-0072098 DMS-0307295 and MacArthur fellowship. 378 HORNG-TZER

• Thạc sĩ - Tiến sĩ - Cao học
• exclusion process
• subjects of mathematics
• Annals of Mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• Research methods
• Data collection methods
• Understanding scientific research
• Ensuring research validity
• Measurement techniques
• Sampling methods
• Scientific research capacity
• Educational institutions
• Policy and management studies
• Vietnam Academy for Ethnic minorities
• Scientific bases
• earth sciences
• Research
• VNU Journal of Science
• scientific reports
• Action research
• linguistics
• research projects
• Foreign Languages
• cooperative research
• Renewable energy
• Introduction to research
• Scientific investigation
• Scientific investigation research
• Experimental designs
• Measurement of variables
• Reading research
• Conducting and reading research
• Research process
• Research report
• Purpose of research
• Scientific method
• Conducting research
• The effect of university autonomy on training and scientific research
• Vietnam national university of agriculture
• Training and scientific research
• Vascular plant
• Flora
• Yen Tu
• Quang Ninh Research Forest
• statements and documents scientific reports
• medical reports
• medical knowledge
• medical research
• clinical trials
• medical management
• health care
• Methods in behavioral research
• Behavioral research
• Scientific understanding
• Fundamental research issues
• Measurement concepts
• Observational methods
• reading comprehension
• education
• optimal picket
• model creation
• urban expansion
• organizing spatial
• Journal of Science
• Journal of Technology
• Technology Management
• Research quality
• Strategy and policy
• Summary of Doctoral thesis
• Summary of Doctoral thesis in public Management
• State management
• Female scientific research human
• Research human resource development
• Scientific research and teaching
• Defense and security education
• Current situation and solutions
• Security education
• Structural biochemistry
• epigenetics
• MicroRNAs
• Tạp chí khoa học
• Tạp chí Công nghệ
• Quản lý công nghệ
• Human resources
• Science management
• Poliomyelitis vaccine Research
• Non Ri Maprec
• Production center