#
Matching, Coupling and Point Processes

Course by
Alexander E. Holroyd
given at the
2009 Cornell Probability Summer School.
### 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**