Warwick EPSRC Symposium on Fluctuation-driven Phenomena and Large Deviations

沃里克 EPSRC 波动驱动现象和大偏差研讨会

基本信息

批准号：
EP/M003620/1
负责人：
Colm Connaughton
金额：
$ 20.58万
依托单位：
University of Warwick
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2015
资助国家：
英国
起止时间：
2015 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FM003620%2F1
关键词：
Warwick EPSRC Symposium Fluctuation driven

项目摘要

The Warwick EPSRC mathematics symposium is organised annually by the University of Warwick with the support of the EPSRC for the benefit of the mathematical sciences community in the UK. It brings leading national and international experts together with UK researchers in a year-long programme of research activities focused on an emerging theme in the mathematical sciences. The proposed symposium for the 2015-16 academic year will concentrate on the theme of "Fluctuation-driven phenomena and large deviations". In very general terms, the symposium will constitute an interdisciplinary focus on understanding the consequences of the interplay between stochasticity and nonlinearity, a recurrent challenge in many areas of the mathematical sciences, engineering and industry.Stochastic processes play a fundamental role in the mathematical sciences, both as tools for constructing models and as abstract mathematical structures in their own right. When nonlinear interactions between stochastic processes are introduced, however, the rigorous understanding of the resulting equations in terms of stochastic analysis becomes very challenging. Mean field theories are useful heuristics which are commonly employed outside of mathematics for dealing with this problem. Mean field theories in one way or another usually involve replacing random variables by their mean and assuming that fluctuations about the mean are approximately Gaussian distributed. In some cases, such models provide a good description of the original system and can be rigorously justified. In many cases they do not. Understanding the latter case, where mean-field models fail, is the central challenge of this symposium. We use "fluctuation driven phenomena" as a generic term to describe the kinds of effects which are observed when mean field theories fail.The challenges stem from the fact that the rich phenomenology of deterministic nonlinear dynamics (singularities, nonlinear resonance, chaos and so forth) is reflected in the stochastic context by a variety of interesting and sometimes unintuitive behaviours: long range correlations, strongly non-Gaussian statistics, coherent structures, absorbing state phase transitions, heavy-tailed probability distributions and enhanced probabilities of large deviations. Such phenomena are found throughout mathematics, both pure and applied, the physical, biological and engineering sciences as well as presenting particular problems to industrialists and policymakers. Contemporary problems such as the forecasting of extreme weather events, the design of marine infrastructure to withstand so-called "rogue waves", quantifying the probability of fluctuation driven transitions or "tipping points" in the climate system or estimating the redundancy required to ensure that infrastructure systems are resilient to shocks all require a step change in our ability to model and predict such fluctuation-driven phenomena. The programme of research activities constituting this symposium will therefore range from the very theoretical to the very applied.At the theoretical end we have random matrix theory which has recently emerged as a powerful tool for analysing the statistics of stochastic processes which are strongly non-Gaussian without the need to go via perturbative techniques developed in the physical sciences such as the renormalisation group. At the applied end we have questions of existential importance to the insurance industry such as how to cost the risk of extreme natural disasters and quantify their interaction with risks inherent in human-built systems. In between we have research on the connections between large deviation theory and nonequilibrium statistical mechanics, extreme events in the Earth sciences, randomness in the biological sciences and the latest numerical algorithms for computing rare events, a topic which has seen strong growth recent years.

沃里克大学每年在EPSRC的支持下每年组织沃里克EPSRC数学研讨会，以造福英国的数学科学社区。它将领先的国家和国际专家与英国研究人员一起参加了为期一年的研究活动计划，该计划重点介绍了数学科学领域的新兴主题。拟议的2015-16学年研讨会将集中在“波动驱动的现象和大偏差”的主题上。从非常一般的角度来看，研讨会将构成跨学科的重点，侧重于理解随机性和非线性之间相互作用的后果，这是数学科学，工程和行业的许多领域的反复挑战。既是构建模型的工具，也可以作为抽象的数学结构本身作为工具。但是，当引入随机过程之间的非线性相互作用时，就随机分析而言，对所得方程的严格理解变得非常具有挑战性。平均场理论是有用的启发式方法，通常在数学以外用于处理此问题。平均场理论以一种或另一种方式通常涉及通过其平均值替换随机变量，并假设对平均值的波动大致分布在平均值上。在某些情况下，这样的模型可以很好地描述原始系统，并且可以严格地证明是合理的。在许多情况下，他们没有。理解后一种情况，即平均场模型失败，是该研讨会的核心挑战。我们使用“波动驱动的现象”作为一个通用术语来描述当平均场理论失败时观察到的效果的种类。挑战源于以下事实：确定性非线性动力学的丰富现象学（奇异性，非线性共振，混乱，混乱等））通过各种有趣的，有时是不直觉的行为反映在随机环境中：远距离相关性，强烈的非高斯统计数据，相干结构，吸收状态相变，重尾概率分布和增强的大偏差概率。在整个数学中都可以找到这种现象，无论是纯净还是应用，物理，生物学和工程科学，以及向工业家和政策制定者提出了特别的问题。当代问题，例如对极端天气事件的预测，海洋基础设施的设计以承受所谓的“流氓波浪”，量化了气候系统中波动驱动的过渡的可能性或“临界点”的可能性，或者确保估算该冗余所需的冗余。基础设施系统对冲击的弹性都需要我们建模和预测这种波动驱动的现象的能力进行逐步改变。因此，构成该研讨会的研究活动计划的范围将从理论上到非常适用的范围。在理论结束时，我们拥有随机的矩阵理论，该理论最近已成为分析随机过程的统计数据的有力工具，这些工具是强烈非高斯的统计数据。不需要通过在物理科学（例如重量法化组）中开发的扰动技术。在所应用的端，我们对保险业有生存重要性的问题，例如如何造成极端自然灾害的风险并量化其与人类建造系统固有的风险的相互作用。在两者之间，我们对大偏差理论与非平衡统计力学，地球科学的极端事件，生物科学的随机性以及计算罕见事件的最新数值算法之间的联系进行了研究，这个话题近年来已经实现了强劲的增长。