Martin T. Barlow: recent preprints, and some older papers.

• [118] M.T. Barlow. Inference for Multiple and Conditional Observers.
  Preprint 2024.
• [117] M.T. Barlow. Pointwise resistance estimates for the Sierpinski carpet.
  Unpublished note (2024).
• [116] M.T. Barlow, N.D. Marshall, R.C. Tyson.
  Optimal shutdown strategies for COVID-19 with economic and mortality costs: British Columbia as a case study.
  Royal Society Open Science (2021). Link to published paper
• [115] M.T. Barlow, D.A. Croydon, T. Kumagai.
  Quenched and averaged tails of the heat kernel of the two-dimensional uniform spanning tree.
  Prob. Th. Rel. Fields (2021). Preprint 2021. Link to published paper
• [114] M.T. Barlow, M. Murugan, Z.-Q. Chen.
  Stability of EHI and regularity of MMD spaces. Preprint 2020.
• [113] M.T. Barlow, D. Karli. Some Boundary Harnack principles with uniform constants.
  Potential Analysis 57 (2022), 433-446. Version 1.
  Link to published paper
• [112] M.T. Barlow. A branching process with contact tracing. Preprint 2020.
  Version 1.
• [111] M.T. Barlow, A.A. Jarai. Geometry of uniform spanning forest components in high dimensions.
  J. Canad. Math. Soc. 71(6), (2019), 1297-1321. Version 1. Version 2.
• [110] M.T. Barlow, M. Murugan. Boundary Harnack principle and elliptic Harnack inequality.
  J. Math. Soc Japan 71 (2019), 383-412. Version 1.
• [109] M.T. Barlow, M. Murugan. Stability of elliptic Harnack inequality.
  Ann. Math. 187 (2018), 777-823.
  (Version 2.)
• [108] M.T. Barlow, D.A. Croydon, T. Kumagai.
  Subsequential scaling limits of simple random walk on the two-dimensional uniform spanning tree
  Ann. Probab. 45 No. 1., 4-55 (2017)
• [107] M.T. Barlow, X. Chen. Gaussian bounds and parabolic Harnack inequality on locally irregular graphs.
  Version 1. Math. Annalen. 366 (3), 1677-1720 (2016).
• [106] M.T. Barlow. Loop Erased Walks and Uniform Spanning Trees.
  MSJ Memoirs 34, 1-32 (2016).
  Correction to Theorem 5.2.
• [105] M.T. Barlow, K. Burdzy, A. Timar.
  Comparison of quenched and annealed invariance principles for random conductance model: Part II.
  Festschrift M. Fukushima, World Scientific 2015.
  Version 1
• [104] O. Angel, M.T. Barlow, O. Gurel-Gurevich, A. Nachmias.
  Boundaries of planar graphs, via circle packings. Version 1.
  Ann. Probab. 44 No. 3. (2016), 1956-1984.
• [103] M.T. Barlow, K. Burdzy, A. Timar.
  Comparison of quenched and annealed invariance principles for random conductance model.
  Prob. Th. Rel. Fields. 164 (2016), 741-770.
  Version 1 . Version 2 (significant changes) .
• [102] M.T. Barlow. Analysis on the Sierpinski carpet.
  Proceedings of SMS Montreal, 2011. CRM Proceedings and Lecture Notes Volume 56, 2013.
• [101] S. Andres, M.T. Barlow.
  Energy inequalities for cutoff functions and some applications.
  J. fur reine angewandte Math. 699 (2015), 183-216. Version 1.
• [100] M.T. Barlow, A. Grigor'yan, T. Kumagai.
  On the equivalence of parabolic Harnack inequalities and heat kernel estimates.
  J. Math. Soc. Japan 64, No. 4 (2012), 1091-1146. Version 1. Version 2.
• [99] S. Andres, M.T. Barlow, J-D Deuschel, B.M. Hambly.
  Invariance principle for the random conductance model.
  Prob. Th. Rel. Fields 156, No. 3--4 (2013), 535-580. Version 1.
• [98] M. T. Barlow, Y. Peres, P. Sousi. Collisions of Random Walks.
  Ann. IHP. Prob. Stat. 48 (2012), 922-946. Version 1 .
• [97] M.T. Barlow and R. Masson.
  Spectral dimension and random walks on the two dimensional uniform spanning tree.
  Comm. Math. Phys. 305 (2011), no 1, 23-57. Version 1.
• [96] M. T. Barlow, J. Ding, A. Nachmias, Y. Peres.
  The evolution of the cover time.
  Combinatorics, Probability and Computing 20 (2011), 331-345. Version 1 .
• [95] M.T. Barlow and R. Masson.
  Exponential tail bounds for loop-erased random walk in two dimensions.
  Ann. Probab. 38 , No. 6, (2010), 2379-2417. ( Older Version 1, Version 2 ) .
• [94] M.T. Barlow and X. Zheng.
  The random conductance model with Cauchy tails.
  Ann. Applied Probability 20 (2010), 869-889.
• [93] M.T. Barlow and J. Cerny.
  Convergence to fractional kinetics for random walks associated with unbounded conductances.
  PTRF 149, (2011), no 3-4, 639-673. Version 1 (pdf) .
  Erratum PTRF 149, (2011), no 3-4, 673-675.
• [92] M. T. Barlow, R. F. Bass, T. Kumagai, A. Teplyaev.
  Uniqueness of Brownian motion on Sierpinski carpets.
  JEMS (Journal Europ. Math. Soc.) 12 (2010), 655-701.
• M. T. Barlow, R. F. Bass, T. Kumagai, A. Teplyaev.
  Supplementary notes for "Uniqueness of Brownian motion on Sierpinski carpets". Unpublished notes.
• [91] M.T. Barlow and J.-D. Deuschel.
  Invariance principle for the random conductance model with unbounded conductances.
  Ann. Probab. 38 (2010), 234-276.
• [90] M.T. Barlow and B. M. Hambly.
  Parabolic Harnack inequality and local limit theorem for percolation clusters.
  Elec. J. Prob. 14 (2009), 1-26.
• [89] M.T. Barlow, R.F. Bass, T. Kumagai.
  Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps
  Mathematische Zeitschrift 261 (2009), 297-320.
  Version 1 (pdf) Version 2 (pdf) . Correction to Proposition 3.3.
• [88] M.T. Barlow, A. Grigor'yan, T. Kumagai.
  Heat kernel upper bounds for jump processes and the first exit time.
  J. fuer Reine und Angewandte Mathematik 626 (2009), 135-157. (pdf)
• [87] M.T. Barlow, R.F. Bass, Z.-Q. Chen, M. Kassmann.
  Non-local Dirichlet Forms and Symmetric Jump Processes.
  Trans. Amer. Math. Soc. 361 (2009), 1963-1999.
  Version 1 (pdf) . Version 2 (pdf) .
• [86] M.T. Barlow, A. A. Jarai, T. Kumagai, G. Slade.
  Random walk on the incipient infinite cluster for oriented percolation in high dimensions.
  Comm. Math. Physics. 278 (2008), 385--431. Version 1 (pdf) . Version 2 (pdf) .
• M.T. Barlow, R.F. Bass, T. Kumagai. Note on the equivalence of parabolic Harnack inequalities and heat kernel estimates
  Unpublished manuscript 2005. (pdf) .
• [85] M.T. Barlow, T. Kumagai. Random walk on the incipient infinite cluster on trees.
  Illinois J. Math. 50 (Doob volume) (2006), 33-65. Version 1.0 (March 2005) (pdf) Version 1.22 (June 2006) (pdf)
• [84] M.T. Barlow, R.F. Bass, T. Kumagai.
  Stability of parabolic Harnack inequalities on metric measure spaces.
  J. Math. Soc. Japan(2) 58 (2006), 485--519.
  Correction to Section 3.
• [83] M.T. Barlow, T. Coulhon and T. Kumagai.
  Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs.
  Comm. Pure Appl. Math. LVIII (2005), 1642-1677. (pdf)
• [82] M.T. Barlow. Anomalous diffusion and stability of Harnack inequalities.
  Surveys in Differential Geometry IX, ed. A. Grigor'yan, S.T. Yau, 1-27 (2005). (pdf)
• [81] M.T. Barlow. Some remarks on the elliptic Harnack inequality.
  Bull. Lond. Math. Soc. 37 (2005), 200-208. (pdf)
• [79] M.T. Barlow. Heat kernels and sets with fractal structure.
  Contemp. Math. 338 (2003) (pdf)
• [78] M.T. Barlow. Random walks on supercritical percolation clusters.
  Ann. Probab. 32 (2004), 3024-3084. (pdf)
• [77] M.T. Barlow and R.F. Bass. Stability of parabolic Harnack inequalities.
  Trans. A.M.S. 356 (2004), 1501-1533.
• [76] M.T. Barlow and S.N. Evans. Markov processes on vermiculated spaces.
  In: Random walks and geometry , ed. V. Kaimanovich, de Gruyter, Berlin, 2004. (pdf)
• [75] M.T. Barlow. Which values of the volume growth and escape time exponent are possible for a graph?
  Revista Math. Iberoamericana. 20 (2004), 1-31. (pdf)
• [74] M.T. Barlow. A diffusion model for electricity prices. Mathematical Finance 12 (2002), 287-298. (pdf)
  Figure 2 of this paper in gif format. (gif)
• [73] S. Athreya, M.T. Barlow, R.F. Bass, E.A. Perkins.
  Degenerate stochastic differential equations and super-Markov chains.
  Probab. Th. Rel. Fields. 123 (2002), 484-520. (pdf)
• [72] M.T. Barlow, T. Kumagai.
  Transition density asymptotics for some diffusion processes with multi-fractal structures.
  Elec. J. Probab. 6 , (2001) paper 9, 1-23. (pdf)
• [71] M. Barlow, K. Burdzy, H. Kaspi, A. Mandelbaum. Coalescence of skew Brownian motions.
  Sem. Prob. XXXV , 202-205. Lect. Notes Math. 1755 , Springer 2001. (pdf)
• [70] M.T. Barlow, R.F. Bass. Divergence form operators on fractal-like domains.
  J. Func. Anal. 175 (2000), 214-247. (pdf)
• [69] M.T. Barlow, T. Coulhon and A. Grigor'yan. Graphs and manifolds with slow heat kernel decay.
  Invent. Math. 144 (2001), 609-649. (pdf)
• [67] M.T. Barlow, R.F. Bass, C. Gui. The Liouville property and a conjecture of De Giorgi.
  Comm. Pure. Appl. Math. LIII (2000), 1007-1038. (pdf)
• [65] M.T. Barlow. On the Liouville property for divergence form operators.
  Canadian J. Math. 50 (1998), 487-496.
• [64] M.T. Barlow, M. Emery, F.B. Knight, S. Song, M. Yor.
  Autour d'um theoreme de Tsirelson sur les filtrations Browniennes et non Browniennes.
  Seminaire de Probabilites XXXII, Lect. Notes Math. 1686, 1998 (pdf)
• [63] M.T. Barlow and R.F. Bass. Random walks on graphical Sierpinski carpets.
  In: Random walks and discrete potential theory, ed. M. Picardello, W. Woess, CUP 1999. (pdf)
• [62] M.T. Barlow. St Flour Lecture Notes: Diffusions on Fractals.
  In: Lect. Notes Math. 1690 . (pdf)
  Letter from George Maxwell. (See Remarks 5.25 (3)). (pdf)
• [61] M.T. Barlow and R.F. Bass. Brownian motion and harmonic analysis on Sierpinski carpets.
  Canadian J. Math. 50 , 673-744 (1999)
• [60] M.T. Barlow and B.M. Hambly.
  Transition density estimates for Brownian motion on scale irregular Sierpinski gaskets.
  Ann. IHP. 33 (1997), 531-557.
• [57] M.T. Barlow, K. Hattori, T. Hattori, H. Watanabe.
  Weak homogenization of anisotropic diffusion on pre-Sierpinski carpets.
  Comm. Math. Phys. 188 (1997), 1-27. (pdf)

  Here are scans of some of my older papers:

• [41] M.T. Barlow and E.A. Perkins. On pathwise uniqueness and expansion of filtrations.
  Sem. Prob. XXIV , 194-209, Lect. Notes Math. 1426 , Springer, Berlin, 1990. (pdf)
• [39] M.T. Barlow and P. Protter. On convergence of semimartingales.
  Sem. Prob. XXIV , 188-193, Lect. Notes Math. 1426 , Springer, Berlin, 1990. (pdf)
• [36] M.T. Barlow, J. Pitman and M. Yor. On Walsh's Brownian Motions.
  Sem. Prob. XXIII , 275-293, Lect. Notes Math. 1372 , Springer, Berlin-New York 1989. (pdf)
• [23] M.T. Barlow, E.A. Perkins and S.J. Taylor. The behaviour and construction of local time for Levy processes.
  Seminar on Stochastic Processes 1984 , 23-54, Birkhauser, Boston 1986 (pdf)
• [20] M.T. Barlow and E.A. Perkins. Levels at which every Brownian excursion is exceptional.
  Sem. Prob. XVIII , 1-28, Lect. Notes in Math. 1059 , Springer, Berlin-New York 1984. (pdf)
• [16] M.T. Barlow and E.A. Perkins. Strong existence, uniqueness and nonuniqueness in an equation involving local time.
  Sem. Prob. XVII , 32-66, Lect. Notes in Math. 986 , Springer, 1983. (pdf)
• [12] M.T. Barlow. L(B(t),t) is not a semi-martingale.
  Sem. Prob. XVI , 209-211, Lect. Notes in Math. 920 , Springer, Berlin 1982. (pdf)
• [10] M.T. Barlow. On Brownian local time. 189-190, Lect. Notes in Math. 850 , Springer, Berlin 1981.
• [9] M.T. Barlow and D.J. Aldous. On countable dense random sets. Sem. Prob. XV 311-327, Lect. Notes in Math. 850 , Springer, Berlin 1981.
• [4] M.T. Barlow, L.C.G. Rogers and D. Williams. Weiner-Hopf factorisation for matrices. Sem. Prob. XIV 324-331, Lect. Notes in Math. 784 , Springer, Berlin, 1980.
  
  NOTE. For published papers, copyright is whatever the appropriate publisher's copyright agreement says it is.

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