TY - JOUR

T1 - The limit shape of random permutations with polynomially growing cycle weights

AU - Cipriani, Alessandra

AU - Zeindler, Dirk

PY - 2015

Y1 - 2015

N2 - In this work we are considering the behaviour of the limit shape of Young diagrams associated to random permutations on the set {1, . . . , n} under a particular class of multiplicative measures with polynomial growing cycle weights. 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

AB - In this work we are considering the behaviour of the limit shape of Young diagrams associated to random permutations on the set {1, . . . , n} under a particular class of multiplicative measures with polynomial growing cycle weights. 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

KW - Random permutation

KW - multiplicative measure

KW - algebraically growing cycle weights

KW - limit shape

KW - functional central limit theorem

KW - saddle point method

M3 - Journal article

VL - 12

SP - 971

EP - 999

JO - Latin American Journal of Probability and Mathematical Statistics

JF - Latin American Journal of Probability and Mathematical Statistics

SN - 1980-0436

IS - 2

ER -