
Kenneth Falconer  Books, Papers, PreprintsLinks to listingsMathSciNet
BooksThe Geometry of Fractal Sets, Cambridge UP, 1985; paperback 1986.Fractal Geometry  Mathematical Foundations and Applications , John Wiley, Third Edition, 2014, with Solutions Manual 3rd Ed. Unsolved Problems in Geometry (with H.T. Croft and R.K. Guy), SpringerVerlag, 1991. Techniques in Fractal Geometry, John Wiley, 1997. Fractals  A Very Short Introduction, Oxford UP, 2013.
Some selected papersThe Hausdorff dimension of selfaffine fractals, Math. Proc. Cambridge Philos. Soc., 103 (1988), 339350.The dimension of selfaffine fractals II, Math. Proc. Cambridge Philos. Soc., 111 (1992), 169179. Bounded distortion and dimension for nonconformal repellers, Math. Proc. Cambridge Philos. Soc. 115 (1994) 315334. The multifractal spectrum of statistically selfsimilar measures, J. Theoretical Probability, 7 (1994) 681702. Probabilistic methods in fractal geometry, Proc. Conf. Fractal Geometry and Stochastics, Finsterbergen 1994, Progress in Probability, 37 (1995), 313. (with P. Mattila) The packing dimension of projections and sections of measures, Math. Proc. Cambridge Philos. Soc., 119 (1996), 695713. (with T.C. O'Neil) Vectorvalued multifractal measures, Proc. Royal. Soc. Ser. A: Math and Phys. Sci., 452 (1996), 14331457. (with J.D. Howroyd) Packing dimensions of projections and dimension profiles, Math. Proc. Cambridge Philos. Soc., 121 (1997), 269286. (with B. Lammering) Fractal properties of generalized Sierpinski triangles, Fractals,6 (1998), 3141. (with M Järvenpää) Packing dimensions of sections of sets, Math. Proc. Cambridge Philos. Soc., 125(1999), 89104. Generalised dimensions of measures on selfaffine sets, Nonlinearity, 12(1999), 877891. Semilinear PDEs on selfsimilar fractals, Commun. Math. Phys. 206(1999), 235245. A nonlinear Mercerian theorem, J. Math. Anal. App. 239(1999), 440448. Representation of families of sets by measures, multifractal analysis and Diophantine approximation, Math. Proc. Cambridge Philos. Soc. 128(2000), 111121. (with J. Lévy Véhel) Horizons of fractional Brownian surfaces, Proc. Roy. Soc. London, Ser. A. 456(2000), 21532177 (with M. Järvenpää and P. Mattila) Examples illustrating the instability of packing dimensions of sections, Real Analysis Exchange, 25 (2000), 629640. (with R.D. Mauldin) Fubinitype theorems for general measure constructions, Mathematika, 47 (2000), 251265. (with J. Hu) Nonlinear diffusion equations on unbounded fractal domains, J. Math. Anal. App., 256(2001), 606624. Tangent fields and the local structure of random fields, J. Theoret. Probab. 15 (2002), 731750. The local structure of random processes, J. London Math. Soc.67 (2003), 657672. Onesided multifractal analysis and points of nondifferentiability of devil's staircases, Math. Proc. Cambridge Philos. Soc. 136 (2004), 167174. Dimensions of intersections and distance sets for polyhedral norms; Real Analysis Exchange, 30(2005),719726. (with J. O'Connor) Symmetry and enumeration of selfsimilar fractals; Bull. London Math. Soc., 39 (2007), 272282. (with C. Fernández) Inference on fractal processes using multiresolution approximation; Biometrika, 94 (2007), 313334. Preprint (with Y. Demichel) The Hausdorff dimension of pulsesum graphs; Math. Proc. Cambridge Philos. Soc., 143 (2007), 145155. Preprint (with J. Miao) Dimensions of selfaffine fractals and multifractals generated by uppertriangular matrices; Fractals, 15 (2007), 289299. Preprint (with J. Miao) Exceptional sets for selfaffine fractals; Math. Proc. Cambridge Philos. Soc., 145 (2008), 669684. Preprint , Cambridge Journals Online (with J. Lévy Véhel) Multifractional, multistable, and other processes with prescribed local form, J. Theor. Probab., 22 (2009), 375401. arXiv, SpringerLink DOI: 10.1007/s1095900801479 (with R. Le Guével and J. Lévy Véhel) Localisable moving average stable and multistable processes, Stochastic Models, 25 (2009), 648672. arXiv (with A. Sloan) Continuity of subadditive pressure for selfaffine sets, Real Analysis Exchange, 34 (2009), 413428. Preprint (with J. Miao) Random subsets of selfaffine fractals, Mathematika, 56 (2010), 6176. Preprint , Cambridge Journals Online Generalised dimensions of measures on almost selfaffine sets, Nonlinearity, 23 (2010), 10471069. arXiv , IOPScience link (with A. Samuel) Dixmier traces and coarse multifractal analysis; Ergodic Theory Dynam. Systems, 31 (2011), 369381, arXiv (with J.M. Fraser) The horizon problem for prevalent surfaces, Math. Proc. Cambridge Philos. Soc., 151 (2011), 355372 , arXiv (with Lining Liu) Multistable processes and localisability, Stochastic Models 28 (2012), 503526, arXiv (with Jiaxin Hu and Yuhua Sun) Inhomogeneous parabolic equations on unbounded metric measure spaces, Proc. Roy. Soc. Edinburgh A Mathematics 142 (2012), 10031025 , arXiv (with J.M. Fraser) The visible part of plane selfsimilar sets, Proc. American Math. Soc. 141 (2013), 269278, arXiv (with G.C. Boore) Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure, Math. Proc. Cambridge Philos. Soc. 154 (2013), 325349 (with Yimin Xiao) Generalized dimensions of images of measures under Gaussian processes, Adv. Math.252 (2014), 492517, arXiv (with Xiong Jin) Exact dimensionality and projections of random selfsimilar measures and sets, J. London Math. Soc. 90 (2014), 388412, arXiv A Holdertype inequality on a regular rooted tree, J. Math. Analysis Appl. 423 (2015), 913923, arXiv (with Xiong Jin) Dimension conservation for selfsimilar sets and fractal percolation, Int. Math. Res. Notices, 2015(24) (2015), 1326013289, arXiv Higher moments for random multiplicative measures, J. Fractal Geometry 2 (2015), 229247, arXiv (with J.M. Fraser and Xiong Jin) Sixty years of fractal projections, in Fractal Geometry and Stochastics V, Progress in Probability 70, pp.325, Birkhauser (2015), arXiv From fractional Brownian motion to multifractional and multistable motion, in Benoit Mandelbrot  A Life in Many Dimensions, pp.239256, World Scientific, 2015 (with Casey Donoven) Codimension formulae for the intersection of fractal subsets of Cantor spaces, Proc. Amer. Math. Soc 144 (2016), 651663, arXiv (with Pertti Mattila) Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes, J. Fractal Geometry 3 (2016), 319329, arXiv (with Tom Kempton) The dimension of projections of selfaffine sets and measures, Annales Academiae Scientiarum Fennicae  Mathematica 42 (2017), 473486, arXiv (with Tom Kempton) Planar selfaffine sets with equal Hausdorff, box and affinity dimensions, Ergodic Theory and Dynamical Systems 38 (2018), 12891341, arXiv (with J. Lévy Véhel) Selfstabilizing processes, Stochastic Models 34 (2018), 409434, arXiv (with V. Beresnevich, S. Velani, and A. Zafeiropoulos) Marstrand's Theorem revisited: projecting sets of dimension zero, J. Math. Analysis Appl. 472 (2019), 18201845 arXiv (with Xiong Jin) Exact dimensionality and projection properties of Gaussian multiplicative chaos measures, Trans. Amer. Math. Soc. 372 (2019), 29212957 arXiv (with J. Fraser, and T. Kempton) Intermediate dimensions, Math. Zeit. 296 (2019) arXiv (with J. Lévy Véhel) Selfstabilizing processes based on random signs, J. Theoret. Probab. 33 (2020), 134152, A capacity approach to box and packing dimensions of projections and other images, in Analysis, Probability and Mathematical Physics on Fractals, World Scientific (2020), arXiv A capacity approach to box and packing dimensions of projections of sets and exceptional directions, J. Fractal Geom. 8 (2021), 126 arXiv (with S. Burrell, and J. Fraser) Projection theorems for intermediate dimensions, J. Fractal Geom. 8 (2021), 95116 arXiv (with J. Fraser and P. Shmerkin) Assouad dimension influences the box and packing dimensions of orthogonal projections, J. Fractal Geom. 8 (2021), 247259 arXiv (with J. Fraser and L. Lee) Lqspectra of measures of planar nonconformal atractors, Ergodic Theory Dynam. Systems. 41 (2021), 32883306 arXiv Intermediate dimensions  a survey, Thermodynamic Formalism: CIRM JeanMorley Chair, Fall 2019. Pollicott, M. & Vaienti, S. (eds.). Springer, 469493 (Lecture Notes in Mathematics; vol. 2290), 2021. arXiv Intermediate dimension of images of sequences under fractional Brownian motion, Statist. Probab. Lett. 182 (2021), 109300 arXiv Preprints(with A. Yavicoli) Sets with large density at infinity contain all large copies of finite sets, to appear J. d'Analyse Math. arXiv (with A. Yavicoli) Intersections of thick compact sets in R^{d}, to appear Math. Zeit. arXiv (with J. Fraser and A. Käenmäki) Minkowski dimension for measures. arXiv
