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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.

华威 EPSRC 数学研讨会每年由华威大学在 EPSRC 的支持下举办，以造福英国数学科学界。它汇集了领先的国内和国际专家以及英国研究人员，开展为期一年的研究活动计划，重点关注数学科学的新兴主题。 2015-16学年拟议的研讨会将集中讨论“波动驱动现象和大偏差”的主题。一般来说，本次研讨会将形成一个跨学科的焦点，以了解随机性和非线性之间相互作用的后果，这是数学科学、工程和工业许多领域中反复出现的挑战。随机过程在数学科学中发挥着基础作用，既作为构建模型的工具，又作为抽象的数学结构。然而，当随机过程之间引入非线性相互作用时，根据随机分析严格理解所得方程就变得非常具有挑战性。平均场理论是有用的启发式方法，通常在数学之外用于处理这个问题。平均场理论通常涉及用随机变量的均值替换随机变量，并假设均值的波动近似为高斯分布。在某些情况下，此类模型可以很好地描述原始系统，并且可以得到严格的证明。在许多情况下，他们没有。理解后一种情况，即平均场模型失败的情况，是本次研讨会的核心挑战。我们使用“涨落驱动现象”作为通用术语来描述平均场理论失效时观察到的各种效应。挑战源于这样一个事实：确定性非线性动力学（奇点、非线性共振、混沌等）的丰富现象学在随机环境中通过各种有趣且有时不直观的行为反映出来：长程相关性、强非高斯统计、相干结构、吸收态相变、重尾概率分布和大偏差的增强概率。这种现象在数学（无论是纯数学还是应用数学）、物理科学、生物科学和工程科学中随处可见，并且给实业家和政策制定者带来了特殊的问题。极端天气事件的预测、海洋基础设施的设计以抵御所谓的“异常波浪”、量化气候系统中波动驱动的转变或“临界点”的概率或估计确保基础设施系统能够抵御冲击所需的冗余等当代问题，都需要我们对这种波动驱动现象进行建模和预测的能力发生重大变化。因此，构成本次研讨会的研究活动计划将涵盖从非常理论到非常应用的范围。在理论方面，我们有随机矩阵理论，它最近已成为分析强非高斯随机过程统计的强大工具，而无需使用物理科学中开发的微扰技术，例如重整化群。在应用端，我们面临着对保险业至关重要的问题，例如如何计算极端自然灾害的风险成本并量化其与人造系统固有风险的相互作用。在此期间，我们研究大偏差理论与非平衡统计力学、地球科学中的极端事件、生物科学中的随机性以及计算罕见事件的最新数值算法之间的联系，这一主题近年来增长强劲。