Alexander E. Holroyd

Email: holroyd at microsoft dot com
Telephone: 425 538 5566 Fax (include name/email): 425 936 7329
Office: room 2922, building 99
Mailing Address: 1 Microsoft Way, Redmond, WA 98052, USA

Bootstrap Percolation

Stable Marriage Poisson-Lebesgue

Random Sorting Networks

B-M-L Traffic Model
Gallery Talks Probability in Seattle C.V.

I'm in the Theory Group at Microsoft Research. I'm also an affliate member of the Mathematics Departments at the Universities of British Columbia and Washington, and of the Pacific Institute for Mathematical Sciences.

Research Interests: Probability theory, with emphasis on discrete spatial models, including cellular automata, percolation, matching, coupling.

Papers:

[63] A. E. Holroyd and J. B. Martin. Poisson allocations with bounded connected cells. 2014. [ PDF ]
[62] A. E. Holroyd and T. M. Liggett. Symmetric 1-dependent colorings of the integers. 2014. [ PS | PDF ]
[61] A. E. Holroyd, Y. Peres, and J. E. Steif. Wald for non-stopping times: The rewards of impatient prophets. 2014. [ PDF ]
[60] A. E. Holroyd and T. M. Liggett. Finitely dependent coloring. 2014. [ PS | PDF ]
[59] G. R. Grimmett, A. E. Holroyd, and Y. Peres. Extendable self-avoiding walks. Ann. Inst. Henri Poincaré D, 1(1):61-75, 2014. [ PS | PDF ]
[58] J. Gravner and A. E. Holroyd. Percolation and disorder-resistance in cellular automata. Ann. Probab., 2014. [ PS | PDF ]
[57] G. R. Grimmett, A. E. Holroyd, and G. Kozma. Percolation of finite clusters and infinite surfaces. Mathematical Proceedings of the Cambridge Philosophical Society, 156:263-279, 3 2014. [ PDF ]
[56] A. E. Holroyd and J. Martin. Stochastic domination and comb percolation. Electron. J. Probab., 19:no. 5, 1-16, 2014. [ PS | PDF ]
[55] O. Angel, A. E. Holroyd, G. Kozma, J. Wästlund, and P. Winkler. The phase transition for dyadic tilings. Trans. Amer. Math. Soc., 366(2):1029-1046, 2014. [ PS | PDF ]
[54] S. Bereg, A. E. Holroyd, L. Nachmanson, and S. Pupyrev. Drawing permutations with few corners. Graph Drawing, 2013. [ PDF ]
[53] O. Angel, A. E. Holroyd, J. Martin, D. B. Wilson, and P. Winkler. Avoidance coupling. Electron. Commun. Probab., 18:no. 58, 13, 2013. [ PS | PDF ]
[52] A. E. Holroyd and T. Soo. Insertion and deletion tolerance of point processes. Electron. J. Probab., 18:no. 74, 24, 2013. [ PS | PDF ]
[51] K. Bringmann, A. E. Holroyd, K. Mahlburg, and M. Vlasenko. k-run overpartitions and mock theta functions. Quarterly J. Math., 2012. [ PS | PDF ]
[50] O. Angel, V. Gorin, and A. E. Holroyd. A pattern theorem for random sorting networks. Elec. J. Probab., 17(99), 2012. [ PS | PDF ]
[49] S. Pupyrev, L. Nachmanson, S. Bereg, and A. E. Holroyd. Edge routing with ordered bundles. In Graph drawing, volume 7034 of Lecture Notes in Comput. Sci., pages 136-147. Springer, Heidelberg, 2012. [ PDF ]
[48] O. Angel and A. E. Holroyd. Recurrent rotor-router configurations. J. Comb., 3(2):185-194, 2012. [ PS | PDF ]
[47] A. E. Holroyd, F. Ruskey, and A. Williams. Shorthand universal cycles for permutations. Algorithmica, 64(2):215-245, 2012. [ PDF ]
[46] G. R. Grimmett and A. E. Holroyd. Geometry of Lipschitz percolation. Ann. Inst. Henri Poincaré Probab. Stat., 45(2):309-326, 2012. [ PS | PDF ]
[45] G. R. Grimmett and A. E. Holroyd. Lattice embeddings in percolation. Ann. Probab., 40(1):146-161, 2012. [ PS | PDF ]
[44] J. Gravner, A. E. Holroyd, and R. Morris. A sharper threshold for bootstrap percolation in two dimensions. Probab. Theory Related Fields, 153(1-2):1-23, 2012. [ PS | PDF ]
[43] M. Deijfen, O. Häggström, and A. E. Holroyd. Percolation in invariant Poisson graphs with i.i.d. degrees. Arkiv för matematik, 50(1):41-58, 2012. [ PS | PDF ]
[42] R. A. Woodgate and A. E. Holroyd. Correction of Teledyne acoustic doppler current profiler (ADCP) bottom-track range measurements for instrument pitch and roll. 2011. [ PDF ]
[41] A. E. Holroyd. Some circumstances where extra updates can delay mixing. J. Stat. Phys., 145(6):1649-1652, 2011. [ PS | PDF ]
[40] M. Deijfen, A. E. Holroyd, and Y. Peres. Stable Poisson graphs in one dimension. Elec. J. Probab., 16(44):1238-1253, 2011. [ PS | PDF ]
[39] O. Angel and A. E. Holroyd. Rotor walks on general trees. SIAM J. Discrete Math., 25(1):423-446, 2011. [ PS | PDF ]
[38] O. Angel, A. E. Holroyd, and T. Soo. Deterministic thinning of finite Poisson processes. Proc. Amer. Math. Soc., 139(2):707-720, 2011. [ PS | PDF ]
[37] A. E. Holroyd. Geometric properties of Poisson matchings. Probab. Theory Related Fields, 150(3-4):511-527, 2011. [ PS | PDF ]
[36] J. van den Berg, M. R. Hilário, and A. E. Holroyd. Escape of resources in a distributed clustering process. Electronic Communications in Probability, 15(40):442-448, 2010. [ PS | PDF ]
[35] A. Holroyd, F. Ruskey, and A. Williams. Faster generation of shorthand universal cycles for permutations. In Computing and combinatorics, volume 6196 of Lecture Notes in Comput. Sci., pages 298-307. Springer, Berlin, 2010. [ PS | PDF ]
[34] N. Dirr, P. W. Dondl, G. R. Grimmett, A. E. Holroyd, and M. Scheutzow. Lipschitz percolation. Elec. Comm. Probab., 15:14-21, 2010. [ PS | PDF ]
[33] G. R. Grimmett and A. E. Holroyd. Plaquettes, spheres, and entanglement. Electronic Journal of Probability, 15(45):1415-1428, 2010. [ PS | PDF ]
[32] O. Angel and A. E. Holroyd. Random subnetworks of random sorting networks. Elec. J. Combinatorics, 17(1):N23, 2010. [ PS | PDF ]
[31] A. E. Holroyd and J. Propp. Rotor walks and Markov chains. In Algorithmic Probability and Combinatorics, volume 520 of Contemporary Mathematics, pages 105-126. Amer. Math. Soc., 2010. [ PS | PDF ]
[30] O. Angel, A. E. Holroyd, J. B. Martin, and J. Propp. Discrete low-discrepancy sequences. 2009. [ PS | PDF ]
[29] A. E. Holroyd, R. Lyons, and T. Soo. Poisson splitting by factors. Annals of Probability, 2009. [ PS | PDF ]
[28] A. E. Holroyd and T. Soo. A nonmeasurable set from coin flips. Amer. Math. Monthly, 116(10):926-928, 2009. [ PS | PDF ]
[27] C. Hoffman, A. E. Holroyd, and Y. Peres. Tail bounds for the stable marriage of Poisson and Lebesgue. Canad. J. Math., 61(6):1279-1299, 2009. [ PS | PDF ]
[26] O. Angel, A. Holroyd, and D. Romik. The oriented swap process. Ann. Probab., 37(5):1970-1998, 2009. [ PS | PDF ]
[25] A. E. Holroyd, R. Pemantle, Y. Peres, and O. Schramm. Poisson matching. Ann. Inst. Henri Poincaré Probab. Stat., 45(1):266-287, 2009. [ PS | PDF ]
[24] J. Gravner and A. E. Holroyd. Local bootstrap percolation. Electron. J. Probab., 14:no. 14, 385-399, 2009. [ PS | PDF ]
[23] C. Cotar, A. E. Holroyd, and D. Revelle. A percolating hard sphere model. Random Structures Algorithms, 34(2):285-299, 2009. [ PS | PDF ]
[22] A. E. Holroyd, L. Levine, K. Mészáros, Y. Peres, J. Propp, and D. B. Wilson. Chip-firing and rotor-routing on directed graphs. In In and out of equilibrium. 2, volume 60 of Progr. Probab., pages 331-364. Birkhäuser, Basel, 2008. [ PS | PDF ]
[21] A. E. Holroyd. Partition identities and the coin exchange problem. J. Combin. Theory Ser. A, 115(6):1096-1101, 2008. [ PS | PDF ]
[20] J. Gravner and A. E. Holroyd. Slow convergence in bootstrap percolation. Ann. Appl. Probab., 18(3):909-928, 2008. [ PS | PDF ]
[19] A. E. Holroyd. Astonishing cellular automata. Bulletin du Centre de Recherches Mathematiques, 13(1):10-13, 2007. [ PS | PDF ]
[18] O. Angel, A. E. Holroyd, D. Romik, and B. Virág. Random sorting networks. Adv. Math., 215(2):839-868, 2007. [ PS | PDF ]
[17] N. Harvey, A. E. Holroyd, Y. Peres, and D. Romik. Universal finitary codes with exponential tails. Proc. Lond. Math. Soc. (3), 94(2):475-496, 2007. [ PS | PDF ]
[16] C. Hoffman, A. E. Holroyd, and Y. Peres. A stable marriage of Poisson and Lebesgue. Ann. Probab., 34(4):1241-1272, 2006. [ PS | PDF ]
[15] A. E. Holroyd. The metastability threshold for modified bootstrap percolation in d dimensions. Electron. J. Probab., 11:no. 17, 418-433 (electronic), 2006. [ PS | PDF ]
[14] O. Angel, A. E. Holroyd, and J. B. Martin. The jammed phase of the Biham-Middleton-Levine traffic model. Electron. Comm. Probab., 10:167-178 (electronic), 2005. [ PS | PDF ]
[13] A. E. Holroyd and Y. Peres. Extra heads and invariant allocations. Ann. Probab., 33(1):31-52, 2005. [ PS | PDF ]
[12] A. E. Holroyd, T. M. Liggett, and D. Romik. Integrals, partitions, and cellular automata. Trans. Amer. Math. Soc., 356(8):3349-3368 (electronic), 2004. [ PS | PDF ]
[11] A. E. Holroyd. Sharp metastability threshold for two-dimensional bootstrap percolation. Probab. Theory Related Fields, 125(2):195-224, 2003. [ PS | PDF ]
[10] A. E. Holroyd and Y. Peres. Trees and matchings from point processes. Electron. Comm. Probab., 8:17-27 (electronic), 2003. [ PS | PDF ]
[9] A. E. Holroyd. Knotted paths in percolation. J. Statist. Phys., 109(1-2):325-330, 2002. [ PS | PDF ]
[8] A. E. Holroyd. Inequalities in entanglement percolation. J. Statist. Phys., 109(1-2):317-323, 2002. [ PS | PDF ]
[7] A. E. Holroyd. Entanglement and rigidity in percolation models. In In and out of equilibrium (Mambucaba, 2000), volume 51 of Progr. Probab., pages 299-307. Birkhäuser, Boston, MA, 2002. [ PS | PDF ]
[6] A. E. Holroyd and T. M. Liggett. How to find an extra head: optimal random shifts of Bernoulli and Poisson random fields. Ann. Probab., 29(4):1405-1425, 2001. [ PS | PDF ]
[5] A. E. Holroyd. Rigidity percolation and boundary conditions. Ann. Appl. Probab., 11(4):1063-1078, 2001. [ PS | PDF ]
[4] G. R. Grimmett and A. E. Holroyd. Entanglement in percolation. Proc. London Math. Soc. (3), 81(2):485-512, 2000. [ PS | PDF ]
[3] A. E. Holroyd. Existence of a phase transition for entanglement percolation. Math. Proc. Cambridge Philos. Soc., 129(2):231-251, 2000. [ PS | PDF ]
[2] A. E. Holroyd. Percolation Beyond Connectivity. PhD thesis, University of Cambridge, 1999.
[1] A. E. Holroyd. Existence and uniqueness of infinite components in generic rigidity percolation. Ann. Appl. Probab., 8(3):944-973, 1998. [ PS | PDF ]

Student:

Terry Soo, PhD completed April 2010, due to graduate November 2010.


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