PIRE: Percolative and Disordered Systems: A U.S.- Brazil-Netherlands Based International Collaboration

这个PERE项目涉及概率论和统计物理重叠领域的国际研究和教育合作：无序系统、渗流和Schramm-Loewner演化(SLEs)。参与机构包括纽约大学的库兰特数学科学研究所、里约热内卢的国家数学科学研究所和阿姆斯特丹的信息中心。教职员工、博士后和其他科学机构的学生也参与了这一项目的网络和活动(如夏季和冬季学校)。该项目涉及随机空间过程，包括无序系统，如自转眼镜和带有陷阱的随机漫步，以及随机环境中的宏观现象，其中宏观现象自然地表现为微观事件在空间(或时空)中渗透的路径。标度概念和方法在分析这些过程及其相变和临界行为的性质方面发挥着重要作用。PI、共同PI和主要的国际合作者是近年来在渗流及其尺度限制以及自旋玻璃和无序随机行走方面的一些主要进展的主要参与者。在这个项目中涉及的问题包括对现实(即，短程)模型中自旋玻璃转变的渗流特征的分析，以及对二维和更多维的近临界渗流和无序随机游动的标度极限的分析。这些和相关的挑战性问题已经成熟，可以联合来自美国和国外的参与者的不同专业知识进行协作攻击。此外，该项目正在开发的渗流和无序系统的新技术可以应用于各种领域，包括通信、材料科学、神经科学、理论计算机科学和石油工程。该项目侧重于培养具有不同国际教育和研究合作背景的美国学生、博士后研究员和教师。博士后和博士后研究员预计将在国外至少度过一个学期，由其中一名国际合作者和一名Courant教员合作共同指导。其他学生和博士后将被鼓励通过短期访问和参加季节性学校来进行国际合作。拉丁美洲的年度冬季学校(北半球)于2008年1月在智利圣地亚哥开学；欧洲的年度暑期学校于2008年6月在意大利佛罗伦萨的纽约大学校区开学。该项目的一个主要目标是为美国、拉丁美洲和欧洲之间在教职员工、博士后和学生层面加强合作的自我维持模式创造一个制度基础。正在进行接触，争取基金会和业界的支持，以便将从PERE项目中形成的经验转化为在教育和研究方面进行国际合作的自给自足的模式。这个PERE项目由国际科学与工程办公室(OISE)资助，数学部(DMS)共同资助。

This PIRE project involves international research and education collaboration in overlapping areas of probability theory and statistical physics: disordered systems, percolation, and Schramm-Loewner evolutions (SLEs). Participating institutions include the Courant Institute of Mathematical Sciences of New York University, the Instituto Nacional de Matemática Pura e Aplicada of Rio de Janeiro, and the Centrum voor Wiskunde en Informatica of Amsterdam. Faculty, postdocs and students from other scientific institutions are also involved in the networks and activities (such as summer and winter schools) of this PIRE project.The project concerns random spatial processes, including disordered systems such as spin glasses and random walks with traps and in random environments, in which macroscopic phenomena are naturally expressed in terms of paths of microscopic events that percolate through space (or space-time). Scaling concepts and methods play an important role in the analysis of such processes and in the nature of their phase transitions and critical behavior. The PI, co-PIs and key international collaborators have been prime participants in some of the major progress in recent years on percolation and its scaling limits, as well as on spin glasses and disordered random walks. Among the issues addressed in this project are analyses of the percolation signature of the spin glass transition in realistic (i.e., short-range) models and of scaling limits for near-critical percolation and disordered random walks in two and more dimensions. These and related challenging problems are ripe for a collaborative attack combining the diverse expertise of the participants from the U.S. and abroad. Moreover, the new techniques being developed in this project for percolative and disordered systems can be applied in a variety of fields, including communication, materials science, neural science, theoretical computer science and petroleum engineering.This project focuses on training U.S. students, postdoctoral fellows and faculty from various backgrounds in international education and research collaboration. PIRE postdoctoral and predoctoral fellows are expected to spend at least one semester abroad with collaborative joint mentoring by one of the international collaborators together with a Courant faculty member. Other students and postdocs will be encouraged to collaborate internationally via shorter visits and by participating in seasonal schools. A yearly winter (in the Northern hemisphere) school in Latin America starts January, 2008 in Santiago, Chile; a yearly summer school in Europe starts June, 2008 at the NYU campus in Florence, Italy. A major goal of this project is to create an institutional basis for a self-sustaining model of enhanced collaboration at faculty, postdoctoral and student levels between the U.S., Latin America and Europe. Contacts are being made for support from foundations and industry to turn the experience developed from this PIRE project into a self-sustaining model for international collaboration in education and research. This PIRE project is funded by the Office of International Science and Engineering (OISE) with co-funding from the Division of Mathematical Sciences (DMS).