This set of notes explores some of the links between occupation times and Gaussian processes. Notably they bring into play certain isomorphism theorems going back to Dynkin [4], [5] as well as certain Poisson point processes of Markovian loops, which originated in physics through thework of Symanzik [26]. More recently such Poisson gases of Markovian loops have reappeared in the context of the “Brownian loop soup” of Lawler andWerner [16] and are related to the so-called “random interlacements”, see Sznitman [27]. In particular they have been extensively investigated by Le Jan [17], [18]
