The limit distribution of the number of nodes in low strata of a random mapping |
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| Institution: | 1. Center on Frontiers of Computing Studies, Department of Computer Science, Peking University, Beijing 100871, China;2. Department of Materials, University of Oxford, Oxford OX1 3PH, UK;3. Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK;4. Graduate School of China Academy of Engineering Physics, Beijing 100193, China;1. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;2. School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330032, China;3. Tencent Quantum Laboratory, Shenzhen 518000, China;1. Departament d’Enginyeria Electrònica, ETSE-UV, Universitat de València (UV), Spain;2. Departamento de Física Atómica, Molecular y Nuclear, Universidad de Sevilla, 41080 Sevilla, Spain;1. Key Laboratory of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Ministry of Education, Nanjing 210003, China;2. College of Mathematics & Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China |
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| Abstract: | We consider random single-valued mappings of an n-element set into itself. Using simple probabilistic facts, we show that the number of nodes in low strata and the number of cyclic nodes of the graphs of such mappings are identically distributed as n → ∞. |
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