List of publications by Gregory Berkolaiko

Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA Tel: +1-979-845-1924 Fax: +1-979-862-4190 Email: Gregory.Berkolaiko AT math.tamu.edu

Preprint(s)

• G. Berkolaiko, J.M. Harrison, J.H. Wilson, Mathematical Aspects of Vacuum Energy on Quantum Graphs [ PDF, arXiv:0711.2707 [math-ph] ]
• G. Berkolaiko, J.M. Harrison, M. Novaes, Full counting statistics of chaotic cavities from classical action correlations [ PDF, cond-mat/0703803 ]
• G. Berkolaiko, B. Winn, Relationship between scattering matrix and spectrum of quantum graphs [ arXiv:0801.4104v1 [math-ph] ]
• G. Berkolaiko, Two constructions of quantum graphs and two types of spectral statistics, to appear in Proceedings of the Isaac Newton Insitute Programme ``Analysis on Graphs and its Applications'', P. Exner, J. Keating, P. Kuchment, T. Sunada, A.Teplyaev, eds. [ PDF ].
• J.A.D. Appleby, G. Berkolaiko, A. Rodkina, On local stability for a nonlinear difference equation with a non-hyperbolic equilibrium and fading stochastic perturbation, to appear in Journal of Difference Equations and Applications [ PDF ].
• J.A.D. Appleby, G. Berkolaiko, A. Rodkina, Non-exponential stability and decay rates in nonlinear stochastic difference equation with unbounded noises to appear in Stochastics and Stochastics Reports [ PDF, math.PR/0610425 ].

Published papers

• G. Berkolaiko, A lower bound for nodal count on discrete and metric graphs Commun. Math. Phys., 278, 803-819 (2007) [ PDF, math-ph/0611026 ].
• G. Berkolaiko, M. Grinfled, Type of dynamic phase transition in bistable equations, Phys. Rev. E, 76, art.061110 (2007) [ PDF].
• G. Berkolaiko, J.P. Keating, U. Smilansky, Quantum ergodicity for graphs related to interval maps, Commun. Math. Phys., 273, 137-159 (2007) [ PDF, math-ph/0607008 ].
• G. Berkolaiko, Form factor expansion for large graphs: a diagrammatic approach in "Quantum Graphs and Their Applications", (G. Berkolaiko, R. Carlson, S. Fulling and P. Kuchment, eds), Contemp. Math. v.415, AMS, Providence, RI 2006. [ PDF, nlin.CD/0604025 ].
• G. Berkolaiko, A. Rodkina, Almost Sure Convergence of Solutions to Non-Homogeneous Stochastic Difference Equations, J. Difference Equ. Appl. 12 (2006) 535-553 [ PDF, math.PR/0508371 ].
• G. Berkolaiko, M. Grinfled, Multiplicity of periodic solutions in bistable equations, Proc. Roy. Soc. A 462 (2006) 1001-1019 [ gzipped PS, PDF, nlin.CD/0305009 ].
  • An animation of periodic solutions considered in this paper is available here.
• G. Berkolaiko, Diagonal approximation of the form factor of the unitary group, J. Phys. A: Math. Gen. 39 (2006) L77-L84 [ PDF, gzipped PS, nlin.CD/0509037].
• G. Berkolaiko, J.P. Keating, B. Winn, No quantum ergodicity for star graphs, Commun. Math. Phys. 250 259-285 (2004) [ PDF, gzipped PS, math-ph/0308005 ].
• G. Berkolaiko, Form factor for large quantum graphs: evaluating orbits with time-reversal, Waves in Random Media 14 S7-S27 (2004) [ PDF, gzipped PS, nlin.CD/0305009 ].
• G. Berkolaiko, J.P. Keating, B. Winn, Intermediate wave-function statistics, Phys. Rev. Lett. 91 134103 (2003) [ PDF, gzipped PS, nlin.CD/0304034 ].
• G. Berkolaiko, H. Schanz, R.S. Whitney, Form factor for a family of quantum graphs: An expansion to third order, J. Phys. A 36 8373-8392 (2003) [ PDF, gzipped PS, nlin.CD/0205014 ].
• G. Berkolaiko, H. Schanz, R.S. Whitney, Leading off-diagonal correction to the form factor of large graphs, Phys. Rev. Lett. 82 104101 (2002) [PDF, gzipped PS, nlin.CD/0107056 ].
• A. Ordemann, E. Tomer, G. Berkolaiko, S. Havlin, A. Bunde, Structural properties of self-attracting walks, Phys. Rev. E 64 046117 (2001) [PDF, gzipped PS ].
• G. Berkolaiko, Spectral gap of doubly stochastic matrices generated from equidistributed unitary matrices, J. Phys. A 34 (22) 319-326 (2001) [PDF, gzipped PS, nlin.CD/0104009 ].
• G. Berkolaiko, E.B. Bogomolny, J.P. Keating, Star graphs and Seba billiards, J. Phys. A 34 (3) 335-350 (2001) [PDF, gzipped PS, nlin.CD/0010045 ].
• A. Ordemann, G. Berkolaiko, S. Havlin, A. Bunde, Swelling-collapse transition of self-attracting walks, Phys. Rev. E 61 (2) R1005-R1007 (2000) [PDF, gzipped PS].
• G. Berkolaiko, J.P. Keating, Two-point spectral correlations for star graphs, J. Phys. A 32 (45) 7827-7841 (1999) [PDF, gzipped PS].
• G. Berkolaiko, Dynamics of piecewise linear interval maps with hysteresis, Dynamics and Stability of Systems 14 (1) 57-70 (1999) [PDF, gzipped PS].
• G. Berkolaiko, S. Havlin, Number of distinct sites visited by Lévy flights injected into a d-dimensional lattice, Phys. Rev. E 57 (3) 2549-2552 (1998) [PDF, gzipped PS].
• G. Berkolaiko, S. Rabinovich, S. Havlin, Analysis of Carleman Representation of Analytical Recursions , J. Math. Anal. Appl. 224 (1) 81-90 (1998) [PDF, gzipped PS].
• G. Berkolaiko, S. Havlin, Territory covered by N Lévy flights on d-dimensional lattices, Phys. Rev. E 55 (2) 1395-1400 (1997) [PDF, gzipped PS].
• S. Rabinovich, G. Berkolaiko, S. Buldyrev, A. Shehter, S. Havlin, Analytical solution of the logistic equation, Int. J. Bifurcation and Chaos 7 (4) 837-838 (1997).
• G. M. Berkolaiko, On a Peetre Functional, Mathematical Notes 61 (1) 22-28 (1997).
• S. Rabinovich, G. Berkolaiko, S. Havlin, Solving nonlinear recursions, J. Math. Phys. 37 (11) 5828-5836 (1996) [PDF, gzipped PS].
• G. Berkolaiko, S. Havlin, H. Larralde, G. H. Weiss Expected number of distinct sites visited by N Lévy flights on a one-dimensional lattice, Phys. Rev. E 53 (6) 5774-5778 (1996) [PDF, gzipped PS].
• S. Rabinovich, G. Berkolaiko, S. Buldyrev, A. Shehter, S. Havlin, `Logistic Map': an Analytical Solution, Physica A 218 (3-4) 457-460 (1995) [ PDF, gzipped PS].

Books edited

• "Quantum Graphs and Their Applications", G. Berkolaiko, R. Carlson, S. Fulling and P. Kuchment, eds, Contemp. Math. v.415, AMS, Providence, RI 2006.

Theses

• Quantum Star Graphs and Related Systems, PhD Thesis, University of Bristol, 2000 [ gzipped PS (423K)].
• Dynamics of Piecewise Linear Interval Maps with Hysteresis, MPhil Thesis, University of Strathclyde, 1997 [ gzipped PS (178K)].

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This file was last modified on Monday, 09-Jun-2008 16:27:57 CDT.