Coupled connected clusters of the origin for the orthant model (a 2-dimensional degenerate random environment) as p changes from 0 to 1.	Mark Holmes     Statistics Dept., U. Auckland     Private Bag 92019     Auckland 1142, New Zealand       Phone: +649 3737599 x88679     Fax:     +649 3737018       Email:     mholmes{at}stat.auckland.ac.nz                   Curriculum Vitae      Papers      Links	The (random) set of vertices that the origin can reach is green. The set of vertices that can reach the origin is red. The intersection of the two is blue.

Research interests.

My current interests lie in the realm of self-interacting random walks, including random walks in random media. I am also interested in percolation-type models (random media!), measure-valued processes, empirical processes, the lace expansion, and applications of probability.

Probability Theory papers

Holmes, M.P.,   Jarai, A.A.,   Sakai, A., and Slade, G.   High dimensional graphical networks of self-avoiding walks.  Canad. J. Math. 56:77--114, (2004).(pdf)

Holmes, M.P.,   Perkins, E.,   Weak convergence of measure-valued processes and r-point functions.  Annals of Probability 35 (2007) pp1769--1782 (pdf)

Holmes, M.P.,   Sakai, A.,     Senile reinforced random walks. Stochastic Processes and their Applications 117 (2007) pp1519-1539 (pdf)

Holmes, M.P.,     Convergence of lattice trees to super-Brownian motion above the critical dimension. Electronic J. of Probability 13 (2008) pp671-755(pdf)

van der Hofstad, R.   Holmes, M.P.   and   Slade, G. An extension of the inductive approach to the lace expansion. Electronic Communications in Probability 13:291--301, (2008).(pdf)

Holmes, M.P.   The scaling limit of senile reinforced random walk. Electronic Communications in Probability 14:104-115 (2009).(pdf)

van der Hofstad, R.,   and    Holmes, M.P.,   Monotonicity for excited random walk in high dimensions Probability Theory and Related Fields 147:333-348, 2010(pdf)

van der Hofstad, R.,   and    Holmes, M.P.,   An expansion for self-interacting random walks Brazilian Journal of Probability and Statistics 26:1-55, 2012(pdf)

Holmes, M.,   Excited against the tide: A random walk with competing drifts To appear in Annales de l'Institut Henri Poincare (pdf)

Holmes, M., and Salisbury, T.S.    A combinatorial result with applications to self-interacting random walks. Journal of Combinatorial Theory, Series A 119:460-475, 2012(pdf)

Holmes, M., Sun, R.   A monotonicity property for random walk in a partially random environment to appear in Stochastic Processes and their Applications (pdf)

Statistics and Applied Probability papers

Galbraith, S., and Holmes, M.,   A non-uniform birthday problem with applications to discrete logarithms To appear in Discrete Applied Mathematics (pdf)

Wang, Y., Ziedins, I., Holmes, M. and Challands, N.    Tree-structured Models for Difference and Change Detection in a Complex Environment. To appear in Annals of Applied Statistics, 2012.(pdf)

Chen, Y., Holmes, M., and Ziedins, I.    Monotonicity properties of user equilibrium policies for parallel batch systems. to appear in Queueing Systems (pdf)

Kojadinovic, I. and Holmes, M.  Tests of independence among continuous random vectors based on Cramer-von Mises functionals of the empirical copula process. J. of Multivariate Analysis 100:1137-1154 (2009)(pdf)

Kojadinovic, I., Yan, J. and Holmes, M.   Fast large-sample goodness-of-fit tests for copulas. Statistica Sinica 21 (2011), 841-871 (pdf)

Preprints

v.d. Hofstad, R. and Holmes, M.,    The survival probability in high dimensions . (pdf)

Holmes, M., and Salisbury, T.S.    Random walks in degenerate random environments . (pdf)

Holmes, M., and Salisbury, T.S.    Degenerate random environments (pdf)

Holmes, M., Kojadinovic, I., Quessy, J.-F.   Nonparametric tests for change-point detection a la Gombay and Horvath (pdf)

Other

van der Hofstad, R.,   Holmes, M.,   and   Slade, G.,   Extension of the generalized inductive approach to the lace expansion  (full version in pdf)

Holmes, M.,  and Salisbury, T.S., Speed calculations for random walks in degenerate random environments   (pdf)

Links

UBC Probability

RSS group EURANDOM

U. Auckland Statistics dept.

An interesting discussion on what student evaluations actually measure