2014/07/07 by Jay Rosen, Rosen, Jay
Mathematics · #60J55 #FOS: Mathematics #Primary 60K99 #Probability (math.PR) #Secondary 60G17 #math.PR #msc:60G17 #msc:60J55 #msc:60K99
paper · pdf · doi:10.48550/arxiv.1407.1559
arxiv created 2014/07/07 · arxiv updated 2014/07/08
These notes originated in a series of lectures I gave in Marseille in May, 2013. I was invited to give an introduction to the isomorphism theorems, originating with Dynkin, which connect Markov local times and Gaussian processes. This is an area I had worked on some time ago, and even written a book about, but had then moved on to other things. However, isomorphism theorems have become of interest once again, both because of new applications to the study of cover times of graphs and Gaussian fields, and because of new isomorphism theorems for non-symmetric Markov processes and their connection with loop soups and Poisson processes. Thus I felt the time was ripe for a new introduction to this topic. In these notes I have tried to preserve the informal atmosphere of the lectures, and often simply refer the reader to my book and other sources for details.