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- ItemFluctuations near the limit shape of random permutations under a conservative measure(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Cipriani, Alessandra; Zeindler, DirkIn this work we are considering the behavior of the limit shape of Young diagrams associated to random permutations on the set {1, . . . , n} under a particular class of multiplicative measures. Our method is based on generating functions and complex analysis (saddle point method). We show that fluctuations near a point behave like a normal random variable and that the joint fluctuations at different points of the limiting shape have an unexpected dependence structure. We will also compare our approach with the so-called randomization of the cycle counts of permutations and we will study the convergence of the limit shape to a continuous stochastic process.