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: berko AT math.tamu.edu

Note: Author ordering is alphabetical (with few obvious exceptions).

Preprint(s)

G. Berkolaiko, J. B. Kennedy, P. Kurasov, D. Mugnolo Impediments to diffusion in quantum graphs: geometry-based upper bounds on the spectral gap, arXiv:2206.10046.
G. Berkolaiko, G. Cox, B. Helffer, M. P. Sundqvist, Computing nodal deficiency with a refined Dirichlet-to-Neumann map, arXiv:2201.06667.
G. Berkolaiko, Y. Canzani, G. Cox, J. L. Marzuola, Spectral minimal partitions, nodal deficiency and the Dirichlet-to-Neumann map: the generic case, arXiv:2201.00773.
G. Berkolaiko, Y. Canzani, G. Cox, J. L. Marzuola, A local test for global extrema in the dispersion relation of a periodic graph, arXiv:2004.12931.

Book

G. Berkolaiko, P. Kuchment, Introduction to Quantum Graphs, Mathematical Surveys and Monographs 186; 270 pp; hardcover. AMS (2013).

Published papers

L. Alon, R. Band, G. Berkolaiko, Universality of nodal count distribution in large metric graphs, Exper. Math. (2022); arXiv:2106.06096.
G. Berkolaiko, P. Kuchment, Spectral shift via "lateral" perturbation, J. Spect. Theor. 12, 83-104 (2022); arXiv:2011.11142.
G. Berkolaiko, M. Ettehad, Three dimensional elastic beam frames: rigid joint conditions in variational and differential formulation, Stud. Appl. Math. (2022); arXiv:2104.01275.
G. Berkolaiko, L. Booton, Convergence of moments of twisted COE matrices, J. Math. Phys. 62, 063502 (2021), Editor's Pick; arXiv:2006.06075.
G. Berkolaiko, A. Parulekar, Locating conical degeneracies in the spectra of parametric self-adjoint matrices, SIAM J. Matrix Anal. Appl. 42(1), 224-242 (2021); arXiv:2001.02753.
G. Berkolaiko, J. L. Marzuola, D. E. Pelinovsky, Edge-localized states on quantum graphs in the limit of large mass, Ann. Inst. H. Poincaré Anal. Non Linéaire 38(5), 1295–1335 (2021). arXiv:1910.03449.
G. Berkolaiko, M. Kha, Degenerate band edges in periodic quantum graphs, Lett. Math. Phys. 110, 2965-2982 (2020), arXiv:2001.03566.
G. Berkolaiko, J.B. Kennedy, P. Kurasov, D. Mugnolo, Surgery principles for the spectral analysis of quantum graphs, Trans. AMS, 372 5153-5197 (2019), arXiv:1807.08183.
G. Berkolaiko, Y. Latushkin, S. Sukhtaiev, Limits of Quantum Graph Operators With Shrinking Edges, Adv. Math. 352, 632-669 (2019), arXiv:1806.00561.
G. Berkolaiko, G. Cox, J. L. Marzuola, Nodal deficiency, spectral flow, and the Dirichlet-to-Neumann map, Lett. Math. Phys. 109, 1611-1623 (2019), arXiv:1805.03145.
G. Berkolaiko, N. Duffield, M. Ettehad, K. Manousakis, Graph Reconstruction from Path Correlation Data, Inverse Problems 35, 015001 (2019), arXiv:1804.04574.
G. Berkolaiko, B. Winn, Maximal scarring for eigenfunctions of quantum graphs, Nonlinearity 31, 4812 (2018), arXiv:1803.08311.
G. Berkolaiko, A. Comech, Symmetry and Dirac points in graphene spectrum, J Spect Theor 8, 1099-1147 (2018), arXiv:1412.8096.
L. Alon, R. Band, G. Berkolaiko, Nodal statistics on quantum graphs, Communications in Mathematical Physics, 362, 909--948 (2018), arXiv:1709.10413 [math-ph].
G. Berkolaiko, W. Liu, Eigenspaces of symmetric graphs are not typically irreducible, Lett Math Phys 108, 1825-1835 (2018), arXiv:1705.01653 [math.SP].
G. Berkolaiko, An elementary introduction to quantum graphs, in "Geometric and Computational Spectral Theory", Contemporary Mathematics, 700, AMS 2017, arXiv:1603.07356 [math-ph].
G. Berkolaiko, J. Kennedy, P. Kurasov, D. Mugnolo, Edge connectivity and the spectral gap of combinatorial and quantum graphs, J. Phys. A 50, 365201 (2017), arXiv:1702.05264 [math.SP].
G. Berkolaiko, W. Liu, Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph, J. Math. Anal. Appl. 455, 803–818 (2016), arXiv:1601.06225 [math-ph].
G. Berkolaiko, J. Irving, Inequivalent Factorizations of Permutations, J. Combin. Theory A 140, 1-37 (2016). arXiv:1405.5255 [math.CO].
R. Band, G. Berkolaiko, T. Weyand, Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs, J. Math. Phys. 56, 122111 (2015), Featured Article, arXiv:1503.07245 [math-ph].
G. Berkolaiko, A. Comech, A. Sukhtaev, Vakhitov-Kolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields, Nonlinearity 28, 577 (2015). arXiv:1306.5150 [math-ph].
G. Berkolaiko, T. Weyand, Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions, Phil. Trans. Roy. Soc. A. 372, 1471-2962 (2014). arXiv:1212.4475 [math-ph].
G. Berkolaiko, J. Kuipers, Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions , J. Math. Phys. 54, 123505 (2013), Featured Article, arXiv:1307.3280 [math-ph].
G. Berkolaiko, Nodal count of graph eigenfunctions via magnetic perturbation, Anal. PDE 6 1213-1233 (2013). arXiv:1110.5373 [math-ph].
G. Berkolaiko, J. Kuipers, Combinatorial theory of the semiclassical evaluation of transport moments I: Equivalence with the random matrix approach, J. Math. Phys. 54, 112103 (2013) [arXiv:1305.4875 [math-ph]].
R. Band, G. Berkolaiko, Universality of the momentum band density of periodic networks, Phys. Rev. Lett., 111 130404 (2013), Editor's Suggestion, arXiv:1304.6028 [math-ph].
G. Berkolaiko, P. Kuchment, Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths, in "Spectral Geometry", edited by A.H. Barnett, C.S. Gordon, P.A. Perry and A. Uribe. Proceedings of Symposia in Pure Mathematics 84 (2012) arXiv:1008.0369 [math-ph].
G. Berkolaiko, A. Comech, On spectral stability of solitary waves of nonlinear Dirac equation in 1D , Mat. Model. Nat. Phenom., 7, 13-31 (2012) arXiv:0910.0917[math-ph]
G. Berkolaiko, P. Kuchment, U. Smilansky, Critical partitions and nodal deficiency of billiard eigenfunctions, Geom. Funct. Anal., 22, 1517-1540 (2012) arXiv:1107.3489 [math-ph]
G. Berkolaiko, J. Kuipers, Universality in chaotic quantum transport: The concordance between random matrix and semiclassical theories, Phys Rev E. 85, 045201(R) (2012), arXiv:1111.4906 [nlin.CD].
G. Berkolaiko, H. Raz, U. Smilansky, Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count, J Phys A: Math Theor, 45, 165203 (2012); Chosen for IOP Select (arXiv:1110.3802 [math-ph]).
R. Band, G. Berkolaiko, H. Raz, U. Smilansky, The number of nodal domains on quantum graphs as a stability index of graph partitions, Comm. Math. Phys., 311, 815-838 (2012) arXiv:1103.1423 [math-ph]
G. Berkolaiko, E. Buckwar, C. Kelly, A. Rodkina, Almost sure asymptotic stability analysis of the theta-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations, LMS J. Comput. Math. 15, 71-83 (2012).
R. Band, G. Berkolaiko, U. Smilansky, Dynamics of nodal points and the nodal count on a family of quantum graphs, Ann. Henri Poincare, 13, 145-184 (2012). arXiv:1008.0505 [math-ph]
G. Berkolaiko, J. Kuipers, Transport moments beyond the leading order, New J. Phys. 13 063020 (2011) arXiv:1012.3526 [nlin.CD]
J. Kuipers, T. Engl, G. Berkolaiko, C. Petitjean, D. Waltner, K. Richter, The density of states of chaotic Andreev billiards, Phys. Rev. B, 83, 195315 (2011) arXiv:1004.1327 [cond-mat]
G. Berkolaiko, B. Winn, Relationship between scattering matrix and spectrum of quantum graphs, Transactions of the AMS, 362, 6261-6277 (2010), PDF, arXiv:0801.4104 [math-ph]
J. Kuipers, D. Waltner, C. Petitjean, G. Berkolaiko, K. Richter, Semiclassical gaps in the density of states of chaotic Andreev billiards , Phys. Rev. Lett. 104, 027001 (2010), PDF, arXiv:0907.2660 [cond-mat]
G. Berkolaiko, J. Kuipers, Moments of the Wigner delay times, J. Phys. A: Math. Theor. 43, 035101 (2010), PDF, arXiv:0910.0060 [nlin.CD]
J.A.D. Appleby, G. Berkolaiko, A. Rodkina, Non-exponential stability and decay rates in nonlinear stochastic difference equation with unbounded noises, Stochastics and Stochastics Reports, 81, 99-127 (2009), PDF, math.PR/0610425.
G. Berkolaiko, J.M. Harrison, J.H. Wilson, Mathematical Aspects of Vacuum Energy on Quantum Graphs, J. Phys. A: Math. Theor. 42, 025204 (2009), PDF, arXiv:0711.2707 [math-ph]
G. Berkolaiko, J.M. Harrison, M. Novaes, Full counting statistics of chaotic cavities from classical action correlations, J. Phys. A: Math. Theor. 41, 365102 (2008); Chosen for IOP Select, PDF, cond-mat/0703803
G. Berkolaiko, Two constructions of quantum graphs and two types of spectral statistics, in ``Analysis on Graphs and its Applications'', P. Exner, J. Keating, P. Kuchment, T. Sunada, A.Teplyaev, eds., Proceeding of Symposia in Pure Mathematics 77, 315-331 (2008) 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, J. Difference Equ. Appl., 14, 923-951 (2008) PDF.
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. Grinfeld, 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 Levy 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 Levy 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 Levy 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 PDF.
Dynamics of Piecewise Linear Interval Maps with Hysteresis, MPhil Thesis, University of Strathclyde, 1997 PDF.

Other work

M. Ettehad, N. Duffield, G. Berkolaiko, Optimizing Consistent Merging and Pruning of Subgraphs in Network Tomography, arXiv:1908.03519.
R. Band, G. Berkolaiko, C.H. Joyner, W. Liu, Quotients of finite-dimensional operators by symmetry representations, arXiv:1711.00918.
G. Berkolaiko, J.M. Harrison, M. Novaes, On inequivalent factorizations of a cycle, PDF, arXiv:0809.3476 [math.CO]

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This file was last modified on Tuesday, 12-Jul-2022 10:59:21 CDT.