I am a Fellow at Emmanuel College, Cambridge and a Research Associate of the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. I completed my PhD at the University of Cambridge under the supervision of Prof. James Norris.
Centre for Mathematical Sciences
Office phone: +44 1223 337952
I spent Lent term 2012 (January to May) at MSRI in Berkeley.
Research interests: Random walks, Brownian motion, mixing times of Markov chains, Poisson Brownian motions, rearrangement inequalities.
2011, 2013, 2015
Intersection and mixing times for reversible chains (2014) (with Yuval Peres, Thomas Sauerwald and Alexandre Stauffer).
Martingale defocusing and transience of a self-interacting random walk (2014) (with Yuval Peres and Bruno Schapira). Ann. Inst. Henri Poincare, accepted.
Dimension of Fractional Brownian motion with variable drift (2013) (with Yuval Peres). Prob. Theory and Related Fields, accepted.
Uniformity of the late points of random walk on Z_n^d for d>=3 (2013) (with Jason Miller).
Total variation cutoff in a tree (2013) (with Yuval Peres). Annales de la Faculte des Sciences de Toulouse
A permuted random walk exits faster (2013) (with Richard Pymar). ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014), no. 1, 185-195.
Mixing times and moving targets (with Peter Winkler). Combin. Probab. Comput., 23 (2014), no. 3, 460-476
Minkowski dimension of Brownian motion with drift (with Philippe Charmoy and Yuval Peres). J. Fractal Geom. 1 (2014), no. 2, 153–176.
Hunter, Cauchy Rabbit, and Optimal Kakeya Sets (with Yakov Babichenko, Yuval Peres, Ron Peretz and Peter Winkler).
Trans. Amer. Math. Soc. 366 (2014), no. 10
On recurrence and transience of self-interacting random walks (with Yuval Peres and Serguei Popov). Bull. Braz. Math. Soci. (N.S.) 44 (2013), no. 4, 841-867.
Symmetric Rearrangements Around Infinity with Applications to Lévy Processes (with Alexander Drewitz and Rongfeng Sun). Probab. Theory and Related Fields, 158 (2014), no. 3-4, 637–664.
The Isolation Time of Poisson Brownian motions (with Yuval Peres and Alexandre Stauffer). ALEA Lat. Am. J. Probab. Math. Stat. 10 (2013), no. 2, 813-829.
Mixing times are hitting times of large sets (2011) (with Yuval Peres). Journal of Theoretical Probability , accepted
An isoperimetric inequality for the Wiener sausage (with Yuval Peres).
Geom. Funct. Anal. 22 (2012), no. 4, 1000-1014.
Collisions of Random Walks (with Martin Barlow and Yuval Peres). Annales de l' Institut Henri Poincare, 48 (2012), no. 4, 922--946.
Mobile Geometric Graphs: Detection, Coverage and Percolation (with Yuval Peres, Alistair Sinclair and Alexandre Stauffer).
Probability Theory and Related Fields, 156 (2013), no. 1-2, 273--305.
Extended abstract appeared in SODA 2011
Brownian motion with variable drift: 0-1 laws, hitting probabilities and Hausdorff dimension (with Yuval Peres).
Math. Proc. Cambridge Philos. Soc. 153 (2012), no. 2, 215-234.
A stochastic epidemiological model and a deterministic limit for BitTorrent-like peer-to-peer file-sharing networks (2008) (with George Kesidis and
Springer Lecture Notes in
Computer Science 2008
ODE approximations to some Markov chain models (2009).
Webpages of coauthors:
Martin Barlow, Philippe Charmoy,
Alexander Drewitz, George Kesidis, Takis Konstantopoulos, Jason Miller, Yuval Peres, Serguei Popov, Richard Pymar, Thomas Sauerwald,
Alistair Sinclair, Alexandre Stauffer, Rongfeng Sun, Peter Winkler