Geodesic
The limit shape of Young diagrams for multiplicative statistics with superpolynomial growth
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IX, Tome 301 (2003), pp. 219-228

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We obtain the limit shape of Young diagrams for a class of multiplicative statistics. In particular, we find the limit shape corresponding to J. Green's function enumerating the characters of $\operatorname{GL}(n, F_q)$. 
@article{ZNSL_2003_301_a7,
     author = {F. V. Petrov},
     title = {The limit shape of {Young} diagrams for multiplicative statistics with superpolynomial growth},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {219--228},
     publisher = {mathdoc},
     volume = {301},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_301_a7/}
}
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F. V. Petrov. The limit shape of Young diagrams for multiplicative statistics with superpolynomial growth. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IX, Tome 301 (2003), pp. 219-228. http://geodesic.mathdoc.fr/item/ZNSL_2003_301_a7/