Dembo, A.; Vershik, A.; Zeitouni, O. Large deviations for integer partitions. (English) Zbl 0972.60006 Markov Process. Relat. Fields 6, No. 2, 147-179 (2000). For an integer \(n\), let \(Q_n\) be the equidistribution on the set of all partitions of \(n\) and \(Q_n^s\) be the equidistribution on the set of all strict partitions of \(n\). A partition \(n_1 \geq n_2 \geq \cdots \geq n_k\) of \(n = \sum_{i=1}^k n_i\) can be identified with a sequence \((r_k)_{k=1,2, \ldots }\) where \(r_k = m\) if exactly \(m\) of the \(n_i\)’s equal \(k\). (A partition is strict if all the \(n_i\)’s are different or, equivalently, all the \(r_k\)’s have value \(0\) or \(1\).) Define the corresponding Young diagram \(\varphi(t) = \sum_{k = [t]}^\infty r_k \), \(t > 0\). Consider the rescaled version \(\tilde\varphi(t) = \varphi([\sqrt{n}t])/\sqrt{n}\). The authors derive large deviation principles of speed \(\sqrt{n}\) for the distributions of \(\tilde\varphi(t)\) under \(Q_n\) and under \(Q_n^s\) in the space of left continuous functions with right limits. They give explicit formulas for the (good) rate functions. The convergence of the distributions of \(\tilde\varphi(t)\) under \(Q_n\) and under \(Q_n^s\) is a consequence of these large deviation principles. A key step in the proof is a different representation of \(Q_n\) and \(Q_n^s\) by means of a conditioning of independent random variables. The methods are not limited to the case of random partitions but extended to so-called \`\` multiplicative statistics\'\'where similar representations are available. Reviewer: Nina Gantert (Berlin) Cited in 38 Documents MSC: 60F10 Large deviations 05A17 Combinatorial aspects of partitions of integers 53A15 Affine differential geometry Keywords:large deviations; Young diagrams; partitions PDFBibTeX XMLCite \textit{A. Dembo} et al., Markov Process. Relat. Fields 6, No. 2, 147--179 (2000; Zbl 0972.60006)