Department of Mathematics and Statistics

Jan De Gier

Publications


Available on arXiv or below.

Preprints


  • Integrable stochastic dualities and the deformed Knizhnik–Zamolodchikov equation, Z. Chen, J. de Gier and M. Wheeler, arXiv:1709.06227; PDF

  • News Articles


  • Melbourne traffic: Trams push cars out of the slow lane on Smith Street, Collingwood, The Age, Jul 17, 2016, Adam Carey; HTML
  • Maths researchers enter the MATRIX to put Australia on the map, Australian Financial Review, Jul 4, 2016, Tim Dodd; HTML
  • Discovery for discovery's sake pays the biggest dividends, Australian Financial Review, Sep 4, 2015, Jan de Gier and Tony Guttmann; HTML
  • Research on the roads: the trouble with traffic, International Innovation 180 (2015); HTML, PDF
  • Trams that never stop at traffic lights could be part of Melbourne's people-moving future, ABC News, 13 February 2015, Loretta Florence; HTML
  • Melbourne trams may never have to stop at traffic lights, under VicRoads plan The Age, 13 february 2015, Marissa Calligeros; HTML
  • Applying physics to better traffic flow, The Australian, Australian IT, 17 January 2012, Jennifer Foreshew; PDF.
  • Going places: why better traffic lights make better sense, The Conversation (19 December 2011), J. de Gier and T.M. Garoni; HTML.
  • Ending traffic jams, Voice 7(12) (2011), Sally Sherwen; HTML.
  • Conference registration deadlines (2010), J. de Gier, and J. Links; PDF
  • Maths Matters: Back to the future, Austms Gazette 35(2) (2008), 79--83, J. de Gier; PDF

  • Research papers


  • A new generalisation of Macdonald polynomials, A. Garbali, J. de Gier and M. Wheeler, Commun. Math. Phys. 352 (2017), 773–804; PDF
  • Finite-size corrections for universal boundary entropy in bond percolation, SciPost Phys. 1, 012 (2016), J. de Gier, J.L. Jacobsen and A. Ponsaing; PDF
  • Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries, J. Phys. A: Math. Theor. 49 (2016), 444002, L. Cantini, A. Garbali, J. de Gier and M. Wheeler; PDF
  • Integrable supersymmetric chain without particle conservation, J. Stat. Mech. (2016) 023104, J. de Gier, G.Z. Feher, B. Nienhuis and M. Rusaczonek; PDF
  • Matrix product and sum rule for Macdonald polynomials, Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics (2016), L. Cantini, J. de Gier and M. Wheeler; PDF; HTML
  • A summation formula for Macdonald polynomials, Lett. Math. Phys. 106 (2016), 381--394 J. de Gier and M. Wheeler; PDF
  • Matrix product formula for Macdonald polynomials, J. Phys. A: Math. Theor. 48 (2015), 384001, L. Cantini, J. de Gier and M. Wheeler; PDF
  • Exclusion in a priority queue, J. Stat. Mech. (2014), P07014, J. de Gier and C. Finn; PDF
  • Traffic disruption and recovery in road networks, Physica A 401 (2014), 82-102, L. Zhang, T.M. Garoni and J. de Gier; PDF
  • The critical fugacity for surface adsorption of SAW on the honeycomb lattice is 1+√2, Comm. Math. Phys. 326 (2014), 727--754, N.R. Beaton, M. Bousquet-Mélou, J. de Gier, H. Duminil-Copin and A.J. Guttmann; PDF
  • Discrete holomorphicity and integrability in loop models with open boundaries, J. Stat. Mech. (2013), P02029, J. de Gier, A. Lee and J. Rasmussen; PDF
  • A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems, L. Zhang, T.M. Garoni and J. de Gier, Transportation Research B: Methodological 49 (2013), 1--23; PDF
  • Off-critical parafermions and the winding angle distribution of the O(n) model, J. Phys. A: Math. Theor. 45 (2012), 275002, A. Elvey Price, J. de Gier, A.J. Guttmann and A. Lee; PDF
  • Deformed Kazhdan-Lusztig elements and Macdonald polynomials, J. Alg. Comb. Theory A 119 (2012), 183-211, J. de Gier, A. Lascoux and M. Sorrell; PDF
  • Relaxation rate of the reverse biased asymmetric exclusion process, J. Phys. A 44 (2011), 405002, J. de Gier, C. Finn and M. Sorrell; PDF
  • Current large deviation function for the open asymmetric simple exclusion process, Phys. Rev. Lett. 107 (2011), 010602, J. de Gier and F.H.L. Essler; PDF.
  • Traffic flow on realistic road networks with adaptive traffic lights, J. Stat. Mech. (2011), P04008, J. de Gier, T.M. Garoni and O. Rojas; PDF
  • Separation of variables for symplectic characters, Lett. Math. Phys. 97 (2011), 61-83, J. de Gier, and A. Ponsaing; PDF
  • Factorised solutions of Temperley-Lieb qKZ equations on a segment, Adv. Theor. Math. Phys. 14 (2010), 795-877, J. de Gier and P. Pyatov; PDF, PS.
  • Combinatorics of Kazhdan-Lusztig elements: Factorisation and fully packed loop models, in Combinatorial representation theory Oberwolfach Reports 7 (2010), 832-835, J. de Gier; PDF
  • Autocorrelations in the totally asymmetric simple exclusion process and Nagel-Schreckenberg model, Phys. Rev. E 82 (2010), 021107, J. de Gier, T. Garoni and Z. Zhou; PDF
  • Exact spin quantum Hall current between boundaries of a lattice strip , Nucl. Phys. B 838 (2010), 371-390, J. de Gier, B. Nienhuis and A. Ponsaing; PDF
  • Exact finite size groundstate of the O(n=1) loop model with open boundaries, J. Stat. Mech. (2009), P04010, 26 pp., J. de Gier, A. Ponsaing and K. Shigechi; PDF
  • Fully packed loop models on finite geometries, Polygons, polyominoes and polycubes, Lecture Notes in Physics 775 (2009), ed. A.J. Guttmann, Ch. 13, 30pp., J. de Gier; PDF
  • Punctured plane partitions and the q-deformed Knizhnik--Zamolodchikov and Hirota equations, J. Alg. Comb. Theory A 116 (2009), 772--794, J. de Gier, P. Pyatov and P. Zinn-Justin; PDF.
  • The two-boundary Temperley-Lieb algebra, J. Algebra 321 (2009), 1132–1167, J. de Gier and A. Nichols; PDF.
  • Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries, J. Phys. A 41 (2008), 485002, 25pp., J. de Gier and F.H.L. Essler; PDF.
  • The Razumov-Stroganov conjecture: Stochastic processes, loops and combinatorics, J. Stat. Mech. (2007), N02001, 6pp., J. de Gier; PDF PS.
  • Exact spectral gaps of the asymmetric exclusion process with open boundaries, J. Stat. Mech. (2006), P12011, 45 pp., J. de Gier and F.H.L. Essler; PDF, PS.
  • Bethe Ansatz solution of the asymmetric exclusion process with open boundaries, Phys. Rev. Lett. 95 (2005), 240601, 4pp., J. de Gier and F.H.L. Essler; PDF, PS.
  • Magic in the spectra of the XXZ quantum chain with boundaries at Delta=0 and Delta=-1/2, Nucl. Phys. B 729 (2005), 387-418, J. de Gier, A. Nichols, P. Pyatov and V. Rittenberg; PDF, PS.
  • One-boundary Temperley-Lieb algebras in the XXZ and loop models, JSTAT (2005), P03003, 30pp., A. Nichols, V. Rittenberg and J. de Gier; PDF, PS.
  • Brauer loops and the commuting variety, J. Stat. Mech. (2005), P01006, 10pp., J. de Gier and B. Nienhuis; PDF, PS.
  • Loops, matchings and alternating-sign matrices, Discr. Math. 298 (2005), 365--388, arXiv:math.CO/0211285, J. de Gier; PDF, PS.
  • Refined Razumov-Stroganov conjectures for open boundaries, J. Stat. Mech. (2004), P09009, 14pp., J. de Gier and V. Rittenberg; PDF, PS.
  • The raise and peel model of a fluctuating interface, J. Stat. Phys. 114 (2004) 1-35, J. de Gier, B. Nienhuis, P. A. Pearce and V. Rittenberg; PDF, PS
  • Exact expressions for correlations in the ground state of the dense O(1) loop model, J. Stat. Mech. (2004), P09010, 24pp., S. Mitra, B. Nienhuis, J. de Gier and M.T. Batchelor; PDF, PS.
  • Nonequilibrium stationary states and equilibrium models with long range interactions, J. Phys. A 37 (2004) 4303-4320, R. Brak, J. de Gier, and V. Rittenberg; PDF, PS.
  • Bethe Ansatz for the Temperley-Lieb loop model with open boundaries, J. Stat. Mech. (2004), P03002, 27pp., J. de Gier and P. Pyatov; PDF
  • Magnetization plateaux in Bethe Ansatz solvable spin-S ladders, Phys. Rev. B 68 (2003), 024418 (1-8), M. Maslen, M.T. Batchelor and J. de Gier; PDF, PS.
  • Stochastic processes and conformal invariance, Phys. Rev. E 67 (2003) 016101-016104, J. de Gier, B. Nienhuis, P. A. Pearce and V. Rittenberg; PDF, PS
  • Temperley-Lieb stochastic processes, J. Phys. A 35 (2002) L661-L668, P. A. Pearce, V. Rittenberg, J. de Gier and B. Nienhuis; PDF, PS.
  • The rotor model and combinatorics, Int. J. Mod. Phys. B 16 (2002) 1883-1889, M.T. Batchelor, J. de Gier and B. Nienhuis; PDF.
  • The XXZ chain at Delta=- 1/2: Bethe roots, symmetric functions and determinants, J. Math. Phys. 43 (2002), 4135-4146, J. de Gier, M.T. Batchelor, B. Nienhuis and S. Mitra; PDF, PS
  • Six - Vertex model with domain wall boundary conditions. Variable inhomogeneities., J. Phys. A 34 (2001) 8135-8144, J. de Gier and V. Korepin; PS.
  • Exactly solvable su(n) mixed spin ladders, J. Stat. Phys. 102 (2001) 559-566, presented at the Baxter Revolution in Mathematical Physics Conference , (2000), M.T. Batchelor, J. de Gier and M. Maslen; PS.
  • Exact stationary state for a deterministic high speed traffic model with open boundaries, J. Phys. A 34 (2001) 3707-3720, J. de Gier; PS.
  • The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions, J. Phys. A 34 (2001) L265-L270, M.T. Batchelor, J. de Gier and B. Nienhuis; PS.
  • Magnetization plateaus in a solvable 3-leg spin ladder, Phys. Rev. B 62 (2000) R3584-R3587, J. de Gier and M.T. Batchelor; PS.
  • Phase diagram of the su(8) quantum spin tube, Phys. Rev. B61 (2000) 15196-15202, J. de Gier, M.T. Batchelor and M. Maslen; PS.
  • Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras, J. Phys. A 33 (2000) L97-L101, M.T. Batchelor, J. de Gier, J. Links and M. Maslen; PS.
  • Exact stationary state for an asymmetric exclusion process with fully parallel dynamics, Phys. Rev. E 59 (1999) 4899-4911, J. de Gier and B. Nienhuis; PS.
  • Bethe Ansatz solution of a decagonal rectangle triangle random tiling, J. Phys. A 31 (1998) 2141-2154, J. de Gier and B. Nienhuis; PS.
  • Solvable rectangle triangle random tilings, Proceedings of the 6th International Conference on Quasicrystals, eds. S. Takeuchi and T. Fujiwara, World Scientific (1998) 91-94, J. de Gier and B. Nienhuis; PS.
  • Integrability of the square-triangle random tiling, Phys. Rev. E 55 (1997) 3926-3933, J. de Gier and B. Nienhuis; PS.
  • The exact solution of an octagonal rectangle-triangle random tiling, J. Stat. Phys. 87 (1997) 415-437, J. de Gier and B. Nienhuis; PS.
  • Exact solution of an octagonal random tiling model, Phys. Rev. Lett. 76 (1996) 2918-2921, J. de Gier and B. Nienhuis; PS.
  • Operator spectrum and exact exponents of the fully packed loop model, J. Phys.A: Math. Gen. 29 (1996) 6489-6504, J. Kondev, J. de Gier and B. Nienhuis; PS.

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