  We describe the central measures for the random walk on graded graphs. Using
this description, we obtain the list of all finite traces on three
infinite-dimensional algebras: on the Brauer algebra, on the partition algebra,
and on the walled Brauer algebra. For the first two algebras, these lists
coincide with the list of all finite traces of the infinite symmetric group.
For the walled Brauer algebra, the list of finite traces coincide with the list
of finite traces of the square of the latter group. We introduce the operation
which corresponds to the graph another graph which called "Pasclization" of the
initial graph and then give the general criteria for coinsidness of the sets of
traces on both graphs.
