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Explore the extension of classical parking functions through a probabilistic parking protocol in this 48-minute USC Probability and Statistics Seminar talk. Delve into the properties of preference vectors as parking functions and examine the impact of the probabilistic parameter p. Discover a sharp transition in parking statistics when p=1/2 and learn how these findings connect to other combinatorial phenomena. Gain insights from the speaker's joint work with Irfan Durmic, Alex Han, Pamela E. Harris, and Rodrigo Ribeiro. If time allows, hear about newer thoughts and potential future research directions in this fascinating area of probability and combinatorics.
