Notes from a graduate course
During the autumn of 2012, I gave a graduate course at the University of Geneva concerning the kinetic limit derivation of Smoluchowski's coagulationdiffusion PDE.
This article developed from notes from the class:
Coagulation and diffusion: a probabilistic perspective on the Smoluchowski PDE.
Probab. Surv., 14, 205288 (2017).
Publications
 Critical exponents in percolation via lattice animals.
Electron. Comm. Probab., 10, no.4, 4559 (2005).
 Fluctuation of planar Brownian loop capturing large area.
With Yuval Peres.
Trans. Amer. Math. Soc., 360, no. 12, 61976230 (2008).
 The kinetic limit of a system of coagulating Brownian particles.
With Fraydoun Rezakhanlou.
Arch. Rational Mech. Anal., 185, 167 (2007).
 Kinetic limit for a system of coagulating planar Brownian particles.
With Fraydoun Rezakhanlou.
J. Stat. Phys., 124, 9971040 (2006).
 Moment bounds for the Smoluchowski equation and their consequences.
With Fraydoun Rezakhanlou.
Comm. Math. Phys., 276, no. 3, 645670 (2007).
 Greedy lattice animals: geometry and
criticality.
Ann. Probab., 34, no.2, 593637, (2006).
 Coagulation, diffusion and the continuous
Smoluchowski equation.
With Mohammad Reza Yaghouti and Fraydoun Rezakhanlou.
Stochastic Process. Appl., 119 , no. 9, 30423080, (2009).
 Monotone loop models and rational resonance.
With Richard Kenyon.
Probab. Theory and Related Fields,
150, no. 34 ,613633, (2011)
 Biased random walks on GaltonWatson trees with
leaves.
With Gerard Ben Arous, Alexander Fribergh and Nina Gantert.
Ann. Probab., 40, no. 1, 280338, (2012).
 Powerlaw Polya's urn and fractional Brownian motion.
With Scott Sheffield.
Probab. Theory and Related Fields, 157, no. 3, 691719, (2013).
 Phase separation in random cluster models I:
uniform upper bounds on local deviation.
Comm. Math Phys., 310 , no. 2, 455509, (2012)
 Phase separation in random cluster models II:
the droplet at equilibrium, and local deviation lower bounds.
Ann. Probab., 40 , no. 3, 921978, (2012)
 Phase separation in random cluster models III:
circuit regularity.
J. Stat. Phys., 142, no. 2, 229276, (2011)
 Randomly biased walks on subcritical trees.
With Gerard Ben Arous.
Comm. Pure Appl. Math., 65 , no. 11, 14811527, (2012)

Stable limit laws for randomly biased walks on supercritical trees.
Ann. Probab., 41 , no. 3A, 16941766, (2013)

Exit time tails from pairwise decorrelation in hidden Markov chains, with applications to dynamical percolation.
With Elchanan Mossel and Gabor Pete.
Electron. J. Probab., 17 , article 68, 116, (2012)

Phase transition for the speed of the biased random walk on the supercritical percolation cluster.
With Alex Fribergh.
Comm. Pure Appl. Math., 67 , no. 2, 173245, (2014)

Infinite cycles in the random stirring model on trees.
Bulletin of the Institute of Mathematics, Academia Sinica, Special Issue in honour of S.R.S. Varadhan's 70th birthday, 8, no. 1, 85104, (2013)

Selfavoiding walk is subballistic.
With Hugo DuminilCopin.
Comm. Math. Phys., 324 , no. 2, 401423, (2013)

Brownian Gibbs property for Airy line ensembles.
With Ivan Corwin.
Invent. Math., 195 , 441508, (2014)

Sharp phase transition in the random stirring model on trees.
Probab. Theory and Related Fields, 161 , no. 34, 429448, (2015)

Local time on the exceptional set of dynamical percolation, and the Incipient Infinite Cluster.
With Gabor Pete and Oded Schramm.
Ann. Probab., 43 , no. 6, 29493005, (2015)

On the probability that selfavoiding walk ends at a given point.
With Hugo DuminilCopin, Alexander Glazman and Ioan Manolescu.
Ann. Probab., 44 , no. 2, 955983, (2016)

KPZ Line Ensemble.
With Ivan Corwin.
Probab. Theory and Related Fields, 166 , no. 12, 67185, (2016)

The competition of roughness and curvature in areaconstrained polymer models.
With Riddhipratim Basu and Shirshendu Ganguly.
Comm. Math. Phys., to appear.

An upper bound on the number of selfavoiding polygons via joining .
Ann. Probab., 46 , no. 1, 175206, (2016)

On selfavoiding polygons and walks: the snake method via pattern fluctuation .
Trans. Amer. Math. Soc., to appear.

On selfavoiding polygons and walks: the snake method via polygon joining .
Electron. J. Probab., to appear.
The next article gathers together the content of the preceding three; it includes some exposition and emphasises some common themes.

On selfavoiding polygons and walks: counting, joining and closing.
Online survey.
 Critical point for infinite cycles in a random loop model on trees.
With Milind Hegde.
Ann. Appl. Probab., to appear.

Selfattracting selfavoiding walk.
With Tyler Helmuth.
Probab. Theory and Related Fields, to appear.

Brownian regularity for the Airy line ensemble, and multipolymer watermelons in Brownian last passage percolation.
Mem. Amer. Math. Soc., to appear.

Modulus of continuity of polymer weight profiles in Brownian last passage percolation.
Ann. Probab., to appear.
Preprints