Matching, Coupling and Point Processes

Exercises | Some slides

Topics

• Point processes, invariance, Poisson process, mass transport, Palm process
• Tail bounds for 2-color and 1-color matching, stable matching, factor matchings
• Allocations, shift-coupling and extra heads, stable allocation
• Multi-color matching, random degrees
• Minimal and planar matchings
• Factors, thinning
• Determinantal point processes

References

• Poisson Matching, A. E. Holroyd, R. Pemantle, Y. Peres & O. Schramm. Annales de l'Institut Henri Poincare (B), to appear
• Foundations of Modern Probability, Olav Kallenberg. 2nd Ed. (2002), Springer.
• College Admissions and the Stability of Marriage, D. Gale, L. S. Shapley. The American Mathematical Monthly, Vol. 69, No. 1. (1962), pp. 9-15.
• A Stable Marriage of Poisson and Lebesgue, C. Hoffman, A. E. Holroyd & Y. Peres. The Annals of Probability, 2006, Vol 34, No 4, 1241-1272.
• Extra Heads and Invariant Allocations, A. E. Holroyd & Y. Peres. The Annals of Probability. 2005, Vol 33, no 1, 31-52.
• Determinantal processes and independence, Ben Hough, Manjunath Krishnapur, Yuval Peres, Balint Virag. Probability Surveys, Vol 3, 206-229, 2006.
• Stationary random graphs with prescribed iid degrees on a spatial Posson process. M. Deijfen. Electronic Communications in Probability 14, 81-89.
• Descending chains, the lilypond model, and mutual nearest neighbour matching. D. J. Daley & G. Last. Adv. Apply Prob., 37, 604-628, 2005.
• Probability on Trees and Networks. by R. Lyons with Y. Peres.
• Random complex zeroes I II III. M Sodin, B Tsirelson
• Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process. Acta Math. To appear. Y. Peres, B. Virag
• Invariant matchings of exponential tail on coin flips in Z^d (preprint). A. Timar
• Multicolor Poisson Matching (in preparation). G. Amir, O. Angel, A. E. Holroyd
• Insertion and deletion tolerance for point processes (in preparation). A. E. Holroyd, T. Soo