Mathav Murugan

Associate Professor and Canada Research Chair in Probability (Tier 2)
Department of Mathematics
University of British Columbia

Office: MATX 1104
Address: Department of Mathematics
University of British Columbia
Vancouver
B.C.
Canada V6T 1Z2
Email: mathav [at] math [dot] ubc [dot] ca
CV

About
I am an Associate Professor at the Department of Mathematics, University of British Columbia. My research lies at the intersection of probability, analysis, and geometry. I am particularly interested in heat kernel estimates and stochastic processes on metric measure spaces and fractals, Dirichlet forms, energy measures and their nonlinear counterparts, random walks and jump processes, and quasiconformal geometry. I received my PhD at Cornell University under the supervision of Laurent Saloff-Coste.



Preprints and Publications

M. Murugan, A simplified characterization of stable-like heat kernel estimates pdf
Submitted

S. Eriksson-Bique, M. Murugan, On the energy image density conjecture of Bouleau and Hirsch pdf
Submitted

M. Murugan, Martingale and analytic dimensions coincide under Gaussian heat kernel bounds pdf
Bulletin des Sciences Mathématiques 204 (2025), Paper No. 103710.

M. Murugan, Diffusions and random walks with prescribed sub-Gaussian heat kernel estimates pdf
Annals of Probability (to appear)

N. Kajino, M. Murugan, Heat kernel for boundary trace of reflected diffusions on uniform domains pdf
Submitted Talk at BIRS

M. Murugan, R. Shimizu, First-order Sobolev spaces, self-similar energies and energy measures on the Sierpinski carpet Long version Shorter version
Communications on Pure and Applied Mathematics 78 (2025), no. 9, 1523--1628. Talk at Quasiworld seminar

M. Murugan, Heat kernel for reflected diffusion and extension property on uniform domains pdf
Probability Theory and Related Fields 190 (2024), no. 1-2, 543--599. Talk at Isaac Newton Institute for Mathematical Sciences

M. Murugan, Conformal Assouad dimension as the critical exponent for combinatorial modulus pdf
Annales Fennici Mathematici 48, 2023 Talk at BIRS

N. Kajino, M. Murugan, On the conformal walk dimension: Quasisymmetric uniformization for symmetric diffusions, pdf
Inventiones Mathematicae 231 (2023) 263--405 Talk at MSRI; Naotaka's talk at PIMS

V. Guan, M. Murugan, J. C. Wei, Helmholtz solution for fractional Laplacian and other related operators, pdf
Comm. Contemp. Math. 25 (2023)

M. T. Barlow, Z.-Q. Chen, M. Murugan Stability of EHI and regularity of MMD spaces, pdf
Submitted

T. Jaschek, M. Murugan, Geometric implications of fast volume growth and capacity estimates, pdf
Adv. Anal. Geom. 3, 2021

G. Liu, M. Murugan, On the comparision between jump processes and subordinated diffusions, pdf
ALEA-Latin American Journal of Probability and Mathematical Statistics 20, 1271-1281 (2023)

G. Liu, M. Murugan, Parabolic Harnack inequality implies the existence of jump kernel, pdf
Potential Analysis 2021

N. Kajino, M. Murugan, On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates, pdf
Annals of Probability 48(6) 2920--2951 2020

M. Murugan, On the length of chains in a metric space, pdf
Journal of Functional Analysis 279(6) 108627 (2020)

M. Murugan, A note on heat kernel estimates, resistance bounds and Poincaré inequality, pdf
Asian Journal of Mathematics Vol. 26, No. 6, pp. 853-866. 2024

M. Murugan, Quasisymmetric uniformization and heat kernel estimates, pdf
Transactions of the American Mathematical Society, 372, (2019), 4177--4209 Talk at IPAM

M. T. Barlow, M. Murugan, Boundary Harnack principle and elliptic Harnack inequality, pdf
Journal of the Mathematical Society of Japan, 71, no. 2 (2019), 383--412

M. T. Barlow, M. Murugan, Stability of the elliptic Harnack inequality, pdf
Annals of Mathematics, 187 (2018), 777–823. Martin's talk at BIRS

M. Murugan, L. Saloff-Coste, Heat kernel estimates for anomalous heavy-tailed random walks, pdf
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 55 (2019) no. 2, 697--719

M. Murugan, L. Saloff-Coste, Davies' method for anomalous diffusions, pdf
Proceedings of the AMS, 145 (2017), no. 4, 1793–1804.

M. Murugan, L. Saloff-Coste, Harnack inequalities and Gaussian estimates for random walks on metric measure spaces, pdf
Electronic Journal of Probability, 28. 1--81 (2023).

L. Levine, M. Murugan, Y. Peres, B. Ugurcan, Divisible sandpile at critical density, pdf
Annales Henri Poincaré 17 (2016), no. 7, 1677–1711

M. Murugan, L. Saloff-Coste, Anomalous threshold behavior of long range random walks, pdf
Electronic Journal of Probability, 20 (2015), no. 74, 1–21.

M. Murugan, L. Saloff-Coste, Transition probability estimates for long range random walks, pdf
New York Journal of Mathematics, 21 (2015) 723–757.

T. Faver, K. Kochalski, M. K. Murugan, H. Verheggen, E. Wesson, A. Weston, Roundness properties of ultrametric spaces,
Glasgow Mathematical Journal, 56 (2014), no. 3, 519–535.

M. K. Murugan, Supremal p-negative type of vertex transitive graphs,
Journal of Mathematical Analysis and Applications 391 (2012), no. 2, 376–381.

S. S. Adams, M. K. Murugan, Hurwitz-Radon inspired maximal three-dimensional real orthogonal designs,
The Australasian Journal of Combinatorics 54 (2012), 151–162.

S. S. Adams, J. Davis, N. Karst, M. K. Murugan, B. Lee, M. Crawford, C. Greeley, Novel classes of minimal delay and low PAPR rate 1/2 complex orthogonal designs.
IEEE Transactions of Information Theory 57 (2011), no. 4, 2254–2262.

S. S. Adams, N. Karst, M. K. Murugan, The final case of the decoding delay problem for maximum rate complex orthogonal designs,
IEEE Transactions of Information Theory 56 (2010), no. 1, 103–112.

S. S. Adams, M. Crawford, C. Greeley, B. Lee, M. K. Murugan, Multilevel and multidimensional Hadamard matrices,
Designs, Codes and Cryptography, 51 (2009), no. 3, 245–252.



Links
Probability Seminar
UBC Probability Group