Ten Lectures on Random Media
Ten Lectures on Random Media
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随机媒体十讲
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
A. Sznitman
中科院分区：
文献类型：
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作者：
E. Bolthausen;A. Sznitman
在过去的25年里，随机媒体领域一直是人们密集活动的对象。它收集了通常来自物理科学的各种模型，其中某些材料或物质具有缺陷或不均匀性。可以通过使介质随机来考虑该特征。介质中的随机性会导致非常意想不到的效果，特别是在这些模型的大规模行为中。一开始被认为是一个简单的玩具模型最终成为一个重大的数学挑战。经过二十多年的深入研究，在这一领域，某些新的范式和一些一般的方法已经出现，和个别模型的渐近行为的惊人的结果，现在更好地理解在更一般的框架。这本专着产生于DMV讲座随机媒体举行的作者在数学研究所在Oberwolfach在1999年11月，并试图给一个帐户的一些发展领域，特别是在该地区的随机运动在随机介质和平均场自旋玻璃。这将是一个宝贵的资源，研究生和研究人员在概率论和数学物理。
The field of random media has been the object of intensive activity over the last twenty-five years. It gathers a variety of models generally originating from physical sciences, where certain materials or substances have defects or inhomogeneities. This feature can be taken into account by letting the medium be random. Randomness in the medium turns out to cause very unexpected effects, especially in the large-scale behavior of some of these models. What in the beginning was often deemed to be a simple toy-model ended up as a major mathematical challenge. After more than twenty years of intensive research in this field, certain new paradigms and some general methods have emerged, and the surprising results on the asymptotic behavior of individual models are now better understood in more general frameworks. This monograph grew out of the DMV Lectures on Random Media held by the authors at the Mathematical Research Institute in Oberwolfach in November 1999 and tries to give an account of some of the developments in the field, especially in the area of random motions in random media and of mean-field spin glasses. It will be a valuable resource for postgraduates and researchers in probability theory and mathematical physics.