Centre for Mathematical Sciences
Phone: +44 1223 337944
I am a Reader in Probability in the Statistics Laboratory, part of the DPMMS at the University of Cambridge.
I am also a Fellow of Emmanuel College.
Research interests: Random walks, Brownian motion, mixing times of Markov chains, Poisson Brownian motions, rearrangement inequalities, dynamical percolation.
Mixing Times of Markov Chains
Percolation and Random Walks on Graphs
Logarithmic corrections to scaling in the four-dimensional uniform spanning tree (2020) (with Tom Hutchcroft).
Universality of cutoff for graphs with an added random matching (2020) (with Jonathan Hermon and Allan Sly).
Chen-Stein method for the uncovered set of random walk on Z_n^d for d>=3 (with Sam Thomas). Electron. Commun. Probab. 25 (2020), No. 55, 11.
A comparison principle for random walk on dynamical percolation (2019) (with Jonathan Hermon). Ann. Probab., accepted.
Cutoff for Random Walk on Dynamical Erdos-Renyi Graph (2018) (with Sam Thomas). Ann. Inst. Henri Poincaré Probab. Stat., accepted.
Mixing time for random walk on supercritical dynamical percolation (with Yuval Peres and Jeff Steif). Prob. Theory and Related Fields, 176 (2020), no. 3-4, 809-849.
Quenched exit times for random walk on dynamical percolation (2017) (with Yuval Peres and Jeff Steif). Markov Process. Related Fields, accepted.
Capacity of the range of random walk on Z^4 (2016) (with Amine Asselah and Bruno Schapira). Ann. Probab. 47 (2019), no. 3, 1447–1497.
Strong law of large numbers for the capacity of the Wiener sausage in dimension four (2016) (with Amine Asselah and Bruno Schapira). Prob. Theory and Related Fields 173 (2019), no. 3-4, 813–858.
Sensitivity of mixing times in Eulerian digraphs (2016) (with Lucas Boczkowski and Yuval Peres). SIAM J. Discrete Math (SIDMA) 32 (2018), no.1, 624-655.
Capacity of the range of random walk on Z^d (2016) (with Amine Asselah and Bruno Schapira). Trans. Amer. Math. Soc. 370 (2018), no. 11, 7627–7645.
Random walks colliding before getting trapped (2015) (with Louigi Addario-Berry, Roberto I. Oliveira and Yuval Peres). Electron. J. Probab. 21 (2016), Paper No. 42, 19pp.
Intersection and mixing times for reversible chains (2014) (with Yuval Peres, Thomas Sauerwald and Alexandre Stauffer). Electron. J. Probab., 22 (2017), Paper No. 12, 16 pp.
Martingale defocusing and transience of a self-interacting random walk (with Yuval Peres and Bruno Schapira). Ann. Inst. Henri Poincaré Probab. Stat., 52 (2016), no.3, 1009-1022.
Dimension of Fractional Brownian motion with variable drift (with Yuval Peres). Prob. Theory and Related Fields, 165 (2016), no. 3-4, 771–794.
Uniformity of the late points of random walk on Z_n^d for d>=3 (with Jason Miller). Prob. Theory and Related Fields, 167 (2017), no. 3-4, 1001–1056.
Total variation cutoff in a tree (with Yuval Peres). Annales de la Faculte des Sciences de Toulouse
, (6) 24 (2015), no. 4, 763–779.
A permuted random walk exits faster (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). Prob. 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). J. Theoret. Probab. 28 (2015), no. 2, 488–519.
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). Ann. Inst. Henri Poincaré Probab. Stat., 48 (2012), no. 4, 922--946.
Mobile Geometric Graphs: Detection, Coverage and Percolation (with Yuval Peres, Alistair Sinclair and Alexandre Stauffer).
Prob. Theory and Related Fields, 156 (2013), no. 1-2, 273--305.
Extended abstract 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:
Louigi Addario-Berry, Roberto Oliveira, Amine Asselah,
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