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

这个PIRE项目涉及概率论和统计物理学重叠领域的国际研究和教育合作：无序系统，渗透和Schramm-Loewner演化（SLEs）。 参与机构包括纽约大学的柯朗数学科学研究所、里约热内卢的纯粹数学和应用数学研究所和阿姆斯特丹的Wiskunde en Informatica中心。来自其他科学机构的教师、博士后和学生也参与了网络和活动（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，如自旋玻璃和带有陷阱的随机行走，以及在随机环境中，其中宏观现象自然地用渗透过空间（或时空）的微观事件的路径来表达。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中起着重要作用。PI，co-PI和主要的国际合作者一直是近年来在渗流及其标度极限，以及自旋玻璃和无序随机行走方面取得的一些重大进展的主要参与者。在这个项目中解决的问题是分析现实中自旋玻璃化转变的渗流特征（即，短程）模型和近临界渗流和无序随机行走在两个和更多的维度的标度限制。这些以及相关的挑战性问题已经成熟，可以结合美国和国外参与者的各种专业知识进行合作攻击。此外，该项目所开发的新技术可应用于通信、材料科学、神经科学、理论计算机科学和石油工程等多个领域。该项目的重点是培养来自不同背景的美国学生、博士后研究员和教师进行国际教育和研究合作。PIRE博士后和博士前研究员预计将在国外度过至少一个学期，由国际合作者之一与柯朗教职员工一起进行合作联合指导。将鼓励其他学生和博士后通过短期访问和参加季节性学校进行国际合作。拉丁美洲每年一次的冬季（北方）学校于2008年1月在智利的圣地亚哥开始;欧洲每年一次的夏季学校于2008年6月在意大利的佛罗伦萨的纽约大学校园开始。该项目的一个主要目标是为美国、英国和英国之间加强教师、博士后和学生层面合作的自我维持模式创建制度基础。拉丁美洲和欧洲。目前正在进行联系，争取基金会和工业界的支持，以便将该项目的经验转化为国际教育和研究合作的自我维持模式。 该PIRE项目由国际科学与工程办公室（OISE）资助，并由数学科学部（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).