Geodesic
Multiplicative central measures on Schur graph
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 44-52

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We define the Schur graph as the graph of shifted Young diagrams. Multiplicative central measures on this graph have a characteristic property: their transition probabilities differ from those of standard Plancherel's measures by a factor that depends on the added box and on the order of the diagram. We found all such measures and show that they are parametrized by one positive real number. 
@article{ZNSL_1997_240_a2,
     author = {A. M. Borodin},
     title = {Multiplicative central measures on {Schur} graph},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {44--52},
     publisher = {mathdoc},
     volume = {240},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a2/}
}
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A. M. Borodin. Multiplicative central measures on Schur graph. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 44-52. http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a2/