Christoph Richard: Research



Asymptotic Combinatorics and Mathematical Statistical Mechanics

Visit also the research group Statistical Mechanics and Combinatorics of the Department of Mathematics and Statistics, Melbourne, Australia.



C. Richard, U. Schwerdtfeger and B. Thatte, Area limit laws for symmetry classes of staircase polygons,
submitted
, arXiv:0710:4041

C. Richard, Limit distributions and scaling functions, in: Polygons, Polyominoes, and Polyhedra, ed A.J. Guttmann, book in press,
arXiv:0704:0716

C. Richard, On q-functional equations and excursion moments,
Discr. Math. 309 (2009), 207-230math.CO/0503198

C. Richard, I. Jensen and A.J. Guttmann, Area distribution and scaling function for punctured polygons,
Electronic J. Comb. 11 (2008), #R53
math.CO/0701633

C. Richard, Staircase polygons: moments of diagonal lengths and column heights,
J. Phys.: Conf. Ser. 42 (2006), 239-257, math-ph/0605076

C. Richard, I. Jensen and A.J. Guttmann, Scaling prediction for self-avoiding polygons revisited,
J. Stat. Mech.: Theor. Exp. (2004), P08007, cond-mat/0406027

C. Richard, Area distribution of the planar random loop boundary,
J. Phys. A 37 (2004), 4493-4500, cond-mat/0311346

C. Richard and A.J. Guttmann, Poland-Scheraga models and the DNA denaturation transition,
J. Stat. Phys. 115 (2004), 943-965, ESI preprint No. 1305, cond-mat/0302514

C. Richard and U. Grimm, On entropy and letter frequencies of ternary square-free words
Electronic J. Comb. 11 (2004), #R14, ESI preprint No. 1283, math.CO/0302302

C. Richard, I. Jensen and A.J. Guttmann, Scaling function for self-avoiding polygons,
in: D. Iagolnitzer, V. Rivasseau and J. Zinn-Justin (eds), Proceedings of the International
Congress on Theoretical Physics TH2002 (Paris)
, Birkhäuser, Basel (2003), Supplement, pp. 267--277, cond-mat/0302513

A.R. Rogers, C. Richard and A.J. Guttmann, Self-avoiding walks and polygons on quasiperiodic tilings,
J. Phys. A 36 (2003), 6333-6345, cond-mat/0302414

C. Richard, Scaling behaviour of two-dimensional polygon models,
J. Stat. Phys. 108 (2002), 459-493, cond-mat/0202339

C. Richard and P.A. Pearce, Integrable Lattice Realizations of N=1 Superconformal Boundary Conditions,
Nuclear Phys. B 631 (2002), 447-470, hep-th/010983

C. Richard, A.J.  Guttmann and I. Jensen, Scaling function and universal amplitude combinations for self-avoiding polygons,
J. Phys. A 34 (2001), L495-L501, cond-mat/0107329

C. Richard and A.J. Guttmann, q-linear approximants: scaling functions for polygon models,
J. Phys. A 34 (2001), 4783-4796, cond-mat/0109159

C. Richard,  Disorder in the free-fermion case of the eight-vertex model,
in: H-D. Doebner, W. Scherer and C. Schulte (eds), Proc. Group 21 (Goslar),
World Scientific, Singapore (1997), pp. 998-1002



Dynamical Systems and Mathematics of Aperiodic Order

Visit also the research group page of Michael Baake in Bielefeld, Germany.



P. Mueller and C. Richard, Random colourings of aperiodic graphs: Ergodic and spectral properties,
submitted (2007), arXiv:0709.0821

M. Baake, D. Lenz and C. Richard, Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies,
Lett. Math. Phys. 82 (2007), 61-77, arXiv:0706:1677

D. Lenz and C. Richard, Pure point diffraction and cut and project schemes for measures: The smooth case,
Math. Z. 256 (2007), 347-378math.DS/0603453

C. Richard, Dense Dirac combs with pure point diffraction,
J. Math. Phys. 44 (2003), 4436-4449, ESI preprint No. 1275, math-ph/0302049

M. Baake, R.V. Moody, C. Richard and B. Sing, Which Distributions of Matter Diffract? -- Some Answers,
in: H-R. Trebin (ed) Quasicrystals: Structure and Physical Properties, Wiley-VCH, Berlin (2003), pp. 188-207
ESI preprint No. 1260, math-ph/0301019

C. Richard, An alternative description of random tilings,
Ferroelectrics 250 (2001), 169-174

C. Richard, An alternative view on quasicrystalline random tilings
J. Phys. A 32 (1999), 8823-8829, cond-mat/9907262

C. Richard, M. Höffe, J. Hermisson and M. Baake, Random tilings: concepts and examples,
J. Phys. A 31 (1998), 6385-6408, cond-mat/9712267

M. Baake, J. Hermisson, M. Höffe and C. Richard, Random tilings and dimer models,
in: S. Takeuchi and T. Fujiwara  (eds) Proc. Int. Conf. Quasicrystals 6 (Tokyo), World Scientific, Singapore (1998), pp. 128-131

J. Hermisson, C. Richard and M. Baake, A guide to the symmetry structure of quasiperiodic tiling classes,
J. Phys. I France 7 (1997), 1003-1018, mp-arc 02-180



Computer Algebra



C. Richard and A. Weber, A Symbolic Numeric Environment for Analyzing Measurement Data in Multi-Model Settings (Extended Abstract)
CASC'99 proceedings, (1999) Springer Verlag, ISBN 3-540-66047-X

A. Jung, C. Richard and A. Weber A 1999,  A Symbolic Numeric Environment for Analyzing Measurement Data in Multi-Model Settings
WSI-Report 99-9 (1999), ISSN 0946-3852

B. Amrhein, O. Gloor, W. Küchlin, C. Richard and M. Wolff,  Analysis Alive - an Integrated Learning Environment for Higher Mathematics,
in: R.P. Gilbert et al. (eds), Recent developments in complex analysis and computer algebra. Papers presented in special sessions of the ISAAC'97 congress, Newark, DE, June 2-7, 1997. Kluwer Academic Publishers, Dordrecht, Int. Soc. Anal. Appl. Comput. 4 (1999), 13-23

Analysis Alive

M. Wolff, O. Gloor and C. Richard, Analysis Alive - Ein interaktiver Mathematik-Kurs,
(1998), Basel: Birkhäuser, ISBN 3-7643-5966-8


last update: 07.01.08