Stochastic processes, slaves and supersymmetry

Supersymmetry and Supergroups in Stochastic Quantum Physics

Supersymmetry was first applied to high energy physics. In the early eighties, it found a second and very fruitful field of applications in stochastic quantum physics. This relates to Random Matrix Theory, the topic I focus on in this contribution. I review several aspects of more mathematical interest, in particular, supersymmetric extensions of the Itzykson– Zuber and the Berezin–Karpelevich ...

Stochastic Processes ( Fall 2014 ) Spectral representations and ergodic theorems for stationary stochastic processes Stationary stochastic processes

A stochastic process X is strongly stationary if its fdds are invariant under time shifts, that is, for any (finite) n, for any t0 and for all t1, ..., tn ∈ T , (Xt1 , ..., Xtn) and (Xt1+t0 , ..., Xtn+t0) have the same distribution. A stochastic process X is weakly stationary if its mean function is constant and its covariance function is invariant under time shifts. That is, for all t ∈ T , E(...

Probability and Stochastic Processes

Despite our best efforts to eliminate typographical errors, several have been found. If you find others, please let us know at [email protected] or [email protected] Note that in the following, list, the labels are intended to be read in the following way: Page 4 Line +6 means 6 lines down from the top of page 4. Page 8 Line -5 means 5 lines up from the bottom of page 8. Page ...

Probability and Stochastic Processes

Stochastic processes and algorithms