Approximation theorems for random permanents and associated stochastic processes

The limit theorems for certain stochastic processes generated by permanents of random matrices of independent columns with exchangeable components are established. The results are based on the martingale decomposition of a random permanent function similar to the one known for U-statistics and on relating the components of this decomposition to some multiple stochastic integrals.Mathematics Subject Classification (2000): Primary 60F17, 62G20; Secondary 15A15, 15A52Acknowledgement A significant part of this work was completed when the first author was visiting the Center for Mathematical Sciences at the University of Wisconsin-Madison. He would like to express his gratitude to the Center and its Acting Director, Prof. Thomas G. Kurtz, for their hospitality. Thanks are also due to the first authors current host, the Institute for Mathematics and Its Applications at the University of Minnesota. Finally, both authors graciously acknowledge the comments of an anonymous referee on an earlier version of this paper.