  We study edge asymptotics of poissonized Plancherel-type measures on skew
Young diagrams (integer partitions). These measures can be seen as
generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in
resolving Ulam's problem on longest increasing subsequences of random
permutations and the last passage percolation (corner growth) discrete versions
thereof. Moreover they interpolate between said measures and the uniform
measure on partitions. In the new KPZ-like 1/3 exponent edge scaling limit with
logarithmic corrections, we find new probability distributions generalizing the
classical Tracy--Widom GUE, GOE and GSE distributions from the theory of random
matrices.
