  We consider, following the work of S. Kerov, random walks which are
continuous-space generalizations of the Hook Walks defined by
Greene-Nijenhuis-Wilf, performed under the graph of a continual Young diagram.
The limiting point of these walks is a point on the graph of the diagram. We
present several explicit formulas giving the probability densities of these
limiting points in terms of the shape of the diagram. This partially resolves a
conjecture of Kerov concerning an explicit formula for the so-called Markov
transform. We also present two inverse formulas, reconstructing the shape of
the diagram in terms of the densities of the limiting point of the walks. One
of these two formulas can be interepreted as an inverse formula for the Markov
transform. As a corollary, some new integration identities are derived.
