Publications

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  • N. Beaton, G. GRIMMETT, M. Holmes. Alignment Percolation. Mathematical Physics, Analysis and Geometry, 24, 3 (19pp), 2021. doi: 10.1007/s11040-021-09373-7.

  • Christian Hirsch, M. Holmes, Victor Kleptsyn. Absence of warm percolation in the very strong reinforcement regime. Annals of Applied Probability, 31, 199-217, 2021. doi: 10.1214/20-AAP1587.

  • M. Holmes, Thomas S Salisbury. A shape theorem for the orthant model. The Annals of Probability, 49, 1237-1256, 2021. doi: 10.1214/20-aop1476.

  • David Croydon, M. Holmes. Biased Random Walk on the Trace of Biased Random Walk on the Trace of …. Communications in Mathematical Physics, 375, 1341-1372, 2020. doi: 10.1007/s00220-019-03585-3.

  • Norbert Henze, M. Holmes. CURIOSITIES REGARDING WAITING TIMES IN POLYA'S URN MODEL. TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE, 174, 149-154, 2020.

  • G. GRIMMETT, M. Holmes. Non-Coupling from the Past. 77, 471-485, 2020. doi: 10.1007/978-3-030-60754-8_22.

  • M. Holmes, E Perkins. On the range of lattice models in high dimensions. Probability Theory and Related Fields, 941-1009, 2019. doi: 10.1007/s00440-019-00933-1.

  • M. Holmes, P. Taylor. A paradox for expected hitting times. Stochastic Models, 365-377, 2019. doi: 10.1080/15326349.2019.1695136.

  • M. Holmes, D Kious. A Monotonicity Property for Once Reinforced Biased Random Walk on Zd. 300, 255-273, 2019. doi: 10.1007/978-981-15-0302-3_10.

  • N. Beaton, G. GRIMMETT, M. Holmes. Alignment percolation. 2019.

  • A Collevecchio, M. Holmes, D Kious. On the speed of once-reinforced biased random walk on trees. Electronic Journal of Probability, 23, 2018. doi: 10.1214/18-EJP208.

  • M. Holmes, Thomas S Salisbury. Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment. Electronic Journal of Probability, 22, 2017. doi: 10.1214/17-EJP107.

  • M. Holmes, Victor Kleptsyn. Proof of the WARM whisker conjecture for neuronal connections. Chaos, 27, 043104 (10pp), 2017. doi: 10.1063/1.4978683.

  • Remco van der Hofstad, M. Holmes, Edwin A Perkins. A criterion for convergence to super-Brownian motion on path space. The Annals of Probability, 45, 278-376, 2017. doi: 10.1214/14-AOP953.

  • M. Holmes, T Salisbury. Forward Clusters for Degenerate Random Environments. Combinatorics, Probability and Computing, 25, 744-765, 2016. doi: 10.1017/S0963548316000158.

  • Remco van der Hofstad, M. Holmes, Alexey Kuznetsov, Wioletta Ruszel. Strongly reinforced Pólya urns with graph-based competition. The Annals of Applied Probability, 26, 2494-2539, 2016. doi: 10.1214/16-AAP1153.

  • M. Holmes. Backbone scaling for critical lattice trees in high dimensions. Journal of Physics A: Mathematical and Theoretical, 49, 314001, 2016. doi: 10.1088/1751-8113/49/31/314001.

  • M. Holmes, Yevhen Mohylevskyy, Charles M Newman. The Voter Model Chordal Interface in Two Dimensions. Journal of Statistical Physics, 159, 937-957, 2015. doi: 10.1007/s10955-015-1198-9.

  • M. Holmes. On strict monotonicity of the speed for excited random walks in one dimension. Electronic Communications in Probability, 20, 2015. doi: 10.1214/ECP.v20-4212.

  • M. Holmes, Nicholas D Huntington, Rebecca PL Thong, Jason Brady, Yoshihiro Hayakawa, Christopher E Andoniou, Peter Fleming, Wei Shi, G. Smyth, Mariapia A Degli-Esposti, Gabrielle T Belz, Axel Kallies, Sebastian Carotta, Stephen L Nutt. Peripheral natural killer cell maturation depends on the transcription factor Aiolos. EMBO Journal, 33, 2721-2734, 2014. doi: 10.15252/embj.201487900.

  • Remco van der Hofstad, M. Holmes. The survival probability and r-point functions in high dimensions. Annals of Mathematics, 178, 665-685, 2013. doi: 10.4007/annals.2013.178.2.5.

  • M. Holmes, Ivan Kojadinovic, Jean-François Quessy. Nonparametric tests for change-point detection à la Gombay and Horváth. Journal of Multivariate Analysis, 115, 16-32, 2013. doi: 10.1016/j.jmva.2012.10.004.

  • M. Holmes, T. Salisbury. Random Walks in Degenerate Random Environments. Canadian Journal of Mathematics, 66, 1050-1077, 2013. doi: 10.4153/CJM-2013-017-3.

  • M. Holmes, Rongfeng Sun. A monotonicity property for random walk in a partially random environment. Stochastic Processes and their Applications, 122, 1369-1396, 2012. doi: 10.1016/j.spa.2012.01.006.

  • Remco van der Hofstad, M. Holmes. An expansion for self-interacting random walks. Brazilian Journal of Probability and Statistics, 26, 1-55, 2012. doi: 10.1214/10-BJPS121.

  • M. Holmes, T. Salisbury. A combinatorial result with applications to self-interacting random walks. Journal of Combinatorial Theory, Series A, 119, 460-475, 2012. doi: 10.1016/j.jcta.2011.10.004.

  • Y Wang, I Ziedins, M. Holmes, Neil Challands. Tree models for difference and change detection in a complex environment. The Annals of Applied Statistics, 6, 1162-1184, 2012. doi: 10.1214/12-AOAS548.

  • Steven D Galbraith, M. Holmes. A non-uniform birthday problem with applications to discrete logarithms. Discrete Applied Mathematics, 160, 1547-1560, 2012. doi: 10.1016/j.dam.2012.02.019.

  • M. Holmes. Excited against the tide: A random walk with competing drifts. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 48, 745-773, 2012. doi: 10.1214/11-AIHP434.

  • M. Holmes, T. Salisbury. Degenerate random environments. Random Structures & Algorithms, 45, 111-137, 2012. doi: 10.1002/rsa.20473.

  • Y. Chen, M. Holmes, I Ziedins. Monotonicity properties of user equilibrium policies for parallel batch systems. Queueing Systems, 70, 81-103, 2011. doi: 10.1007/s11134-011-9264-8.

  • Ivan Kojadinovic, Jun Yan, M. Holmes. Fast large-sample goodness-of-fit tests for copulas. Statistica Sinica, 21, 841, 2011. doi: 10.5705/ss.2011.037a.

  • Remco van der Hofstad, M. Holmes. Monotonicity for excited random walk in high dimensions. Probability Theory and Related Fields, 147, 333-348, 2009. doi: 10.1007/s00440-009-0215-9.

  • M. Holmes. The scaling limit of senile reinforced random walk.. Electronic Communications in Probability, 14, 104-115, 2009. doi: 10.1214/ECP.v14-1449.

  • Ivan Kojadinovic, M. Holmes. Tests of independence among continuous random vectors based on Cramér–von Mises functionals of the empirical copula process. Journal of Multivariate Analysis, 100, 1137-1154, 2009. doi: 10.1016/j.jmva.2008.10.013.

  • M. Holmes. Convergence of Lattice Trees to Super-Brownian Motion above the Critical Dimension. Electronic Journal of Probability, 13, 671-755, 2008. doi: 10.1214/EJP.v13-499.

  • M. Holmes, Remco van der Hofstad, G. Slade. An extension of the inductive approach to the lace expansion. Electronic Communications in Probability, 13, 291-301, 2008. doi: 10.1214/ECP.v13-1377.

  • C Pridans, M. Holmes, M Polli, JM Wettenhall, A Dakic, LM Corcoran, G. Smyth, SL Nutt. Identification of Pax5 target genes in early B cell differentiation. Journal of Immunology, 180, 1719-1728, 2008. doi: 10.4049/jimmunol.180.3.1719.

  • M. Holmes, A Sakai. Senile reinforced random walks. Stochastic Processes and their Applications, 117, 1519-1539, 2007. doi: 10.1016/j.spa.2007.02.003.

  • M. Holmes, Edwin Perkins. Weak convergence of measure-valued processes and r -point functions. The Annals of Probability, 35, 1769-1782, 2007. doi: 10.1214/009117906000001088.

  • M. Ritchie, J. Silver, Alicia Oshlack, M. Holmes, Dileepa Diyagama, Andrew Holloway, G. Smyth. A comparison of background correction methods for two-colour microarrays. Bioinformatics, 23, 2700-2707, 2007. doi: 10.1093/bioinformatics/btm412.

  • M. Holmes, Antal A Járai, Akira Sakai, G. Slade. High-Dimensional Graphical Networks of Self-Avoiding Walks . Canadian Journal of Mathematics, 56, 77-114, 2004. doi: 10.4153/CJM-2004-005-1.