We consider the Robinson-Schensted-Knuth algorithm applied to a random input and investigate shape of bumping route (in vicinity $y$-axis) when specified number is inserted into large Plancherel-distributed tableau. show that after projective change coordinate system converges in distribution Poisson process.

We obtain an identity between Fredholm determinants of two kinds of operators, one acting on functions on the unit circle and the other acting on functions on a subset of the integers. This identity is a generalization of an identity between a Toeplitz determinant and a Fredholm determinant that has appeared in the random permutation context. Using this identity, we prove, in particular, conver...

We consider the Plancherel measure on irreducible components of tensor powers spinor representation so2n+1. With respect to this measure, probability an is product its multiplicity and dimension, divided by total dimension product. study limit shape highest weight as power N rank n algebra tend infinity with N/n fixed.