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Using Legendre transformation in three variables, including the remaining group parameter, we arrived at linear partial differential equations with constant coefficients which
We are interested here in concentration for the linear statistics of the spectral measure and for the largest eigenvalue of the Wishart matrix Y ∗ Y , where the entries of Y form
Furthermore, we discuss the equivalence of uniqueness criteria for chains and fields and we establish bounds for the continuity rates of the respective systems of
The two best known examples are the sandpile models where so called avalanches spread over macroscopic distances instantaneously, and the forest fire models where beside the
Under the same conditions the finite dimensional distributions of the repeat times converge to the arrival times of suitably modified Poisson processes, and random trees derived
It follows from our Theorem 2.1 that the limit results proved for heights and (or) lengths of excursions for the case of Brownian motion remain valid for similar quantities of
Key words: semimartingales; Gaussian processes; stationary processes; moving averages; stochastic convolutions; non-canonical representations.. AMS 2000 Subject Classification:
Now, in view of the above, in order to solve the problem of orthogonal separability of the cor- responding Hamilton–Jacobi equation and thus find exact solutions to the
