Publications

1. "Renormalization and convergence in law for the derivative of intersection local time in R²", Stochastic Process. Appl., Volume 118, September 2008, pp. 1552-1585.
2. "Proof of a Tanaka-like formula stated by J. Rosen in Séminaire XXXVIII", Séminaire de Probabilités XLI, Lecture Notes in Math., Springer, Berlin, 1934(2008), pp. 199-202.
3. "A conjecture of Biggs concerning the resistance of a distance-regular graph", with Jacobus Koolen, Electron. J. Combin., Vol. 17(1), 2010. (Note: a much simplified proof of the results in this paper can be found at arxiv:1303.5147)
4. "Pascal's Hexagon Theorem implies the Butterfly Theorem", Math. Mag., Vol 84(1), February 2011, pp. 56-62.
5. "A retelling of Newton's work on Kepler's Laws", Expo. Math., Vol. 29(3), 2011, pp. 253-282.
6. "Applying Brownian motion to the study of birth-death chains", Statist. Probab. Lett., Vol. 81(8), 2011, pp. 1173-1178.
7. "On the expected exit time of planar Brownian motion from simply connected domains", Electron. Commun. Probab., Vol. 16, 2011, pp. 652-663.
8. "A rigidity theorem for special families of rational functions", Ann. Acad. Sci. Fenn. Math., Vol. 37(1), 2012, 277-284.
9. "The derivative of the intersection local time of Brownian motion through Wiener chaos", Séminaire de Probabilités XLIV, Lecture Notes in Math., Springer, Berlin, 2046(2012), pp. 141-148.
10. "Birth-death chains and the local time of Brownian motion", Bull. Aust. Math. Soc., Vol. 85(3), 2012, pp. 497-504.
11. "The rate of convergence of the hyperbolic density on sequences of domains", with Nikola Lakic, Conformal dynamics and hyperbolic geometry: a conference in honor of Linda Keen's 70th birthday, Contemp. Math., AMS, Providence, 573(2012), pp. 147-158.
12. "A method for deriving hypergeometric and related identities using the H² Hardy norm of conformal maps", Integral Transforms Spec. Funct., Vol. 24(4), 2013, pp. 302-313.
13. "On electrical resistances on distance-regular graphs", with Jacobus Koolen and Jongyook Park, European J. Combin., Vol. 34(4), 2013, pp. 770-786.
14. "Random walks at random times: convergence to iterated Lévy motion, fractional stable motions, and other self-similar processes", with Paul Jung, Ann. Probab., Vol. 41(4), 2013, pp. 2682-2708.
15. "There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k₂/k, and large diameter", with Jacobus Koolen and Jongyook Park, J. Combin. Theory Ser. B., Vol 103(6), 2013, pp. 733-741.
16. "A probabilistic proof of the open mapping theorem for analytic functions", Bull. Aust. Math. Soc., Vol. 90(1), 2014, 74-76.
17. "On the Tanaka formula for the derivative of self-intersection local time for fractional Brownian motion", with Paul Jung, Stochastic Process. Appl., Vol. 124(11), 2014, 3846-3868.
18. "The exit time of planar Brownian motion and the Phragmén-Lindelöf principle", J. Math. Anal. Appl., Vol. 422(1), 2015, pp. 638-645.
19. "Holder continuity and occupation-time formulas for fBm self-intersection local time and its derivative", with Paul Jung, J. Theoret. Probab., Vol. 28(1), 2015, pp. 299-312.
20. "Rotation numbers and symbolic dynamics", with David Bowman and Ross Flek, Ann. Acad. Sci. Fenn. Math., Vol. 40, 2015, pp. 227-234
21. "A collection of results concerning simple random walks on distance-regular graphs", with Jacobus Koolen, Discrete Math., Vol. 339(2), 2016, pp. 737-744.
22. "Sum rules for effective resistances in infinite graphs", with José Palacios, J. Stat. Mech. Theory Exp., Vol. 2017(4), 043403
23. "On the planar Brownian Green's function for stopping times", to appear in J. Math. Anal. Appl.
24. "Symmetry in the Green's function for birth-death chains", with José Palacios, to appear in Methodol. Comput. Appl. Probab.
25. "On the distribution of planar Brownian motion at stopping times", to appear in Ann. Acad. Sci. Fenn. Math.