Publications : Updated Fall 2011

    Journal Articles (JA)
  1. (with Oscar Bolina, Pierluigi Contucci and Bruno Nachtergaele) Finite-volume excitations of the 111 interface in the quantum XXZ model. Comm. Math. Phys. 212 (2000) 63--91. http://arxiv.org/abs/math-ph/9908018
  2. (with O.~Bolina, P.~Contucci and B.~Nachtergaele) A continuum approximation for the excitations of the $(1, 1, \dots , 1)$ interface in the quantum Heisenberg model. Electron. J. Diff. Eq. 4 (2000) 1--10. http://arxiv.org/abs/math-ph/9909018
  3. (with B.~Nachtergaele) Droplet states in the XXZ Heisenberg chain. Comm. Math. Phys. 216 (2001) 569--607. http://arxiv.org/abs/math-ph/0009002
  4. (with B.~Nachtergaele and Tohru Koma) The spectral gap for the ferromagnetic spin-J XXZ chain. Adv. Theor. Math. Phys. 5 (2001) 1047--1090. http://arxiv.org/abs/math-ph/0110017
  5. (with Wolfgang Spitzer) Improved bounds on the spectral gap above frustration free ground states of quantum spin chains. Lett. Math. Phys. 63 (2003) 251--270. http://arxiv.org/abs/math-ph/0212029
  6. (with Michael Aizenman and Robert Sims) An extended variational principle for the SK spin-glass model. Phys. Rev. B 68 (2003) 214403 (4 pages). http://arxiv.org/abs/cond-mat/0306386
  7. (with B. Nachtergaele and W. Spitzer) Ferromagnetic ordering of energy levels. J. Statist. Phys. 116 (2004) 719--738. http://arxiv.org/abs/math-ph/0308006
  8. (with B. Nachtergaele) A ferromagnetic Lieb-Mattis theorem. Phys. Rev. Lett. 94 (2005) 057206 (4 pages). http://arxiv.org/abs/math-ph/0408020
  9. (with Eugene Kritchevski) The extended variational principle for mean-field, classical spin systems. Rev. Math. Phys. 17 (2005) 1209--1239. http://arxiv.org/abs/math-ph/0505001
  10. (with B. Nachtergaele and W. Spitzer) Droplet excitations for the spin-1/2 XXZ chain with kink boundary conditions. Ann. Henri Poincaré 8 (2007) 165--201. http://arxiv.org/abs/math-ph/0508049
  11. (with Marek Biskup and Lincoln Chayes) Quantum spin systems at positive temperature. Commun. Math. Phys. 69 (2007) 611--657. http://arxiv.org/abs/math-ph/0509017
  12. (with Cristian Giardinà) Variational bounds for the Generalized Random Energy Model. J. Statist. Phys. 127 (2007) 1--20. http://arxiv.org/abs/math-ph/0601068
  13. (with Brigitta Vermesi) Some observations for mean-field spin glass models. Lett. Math. Phys. 83 (2008) 281--303. http://arxiv.org/abs/0707.0031
  14. (with Jaideep Mulherkar, B. Nachtergaele and R. Sims) Isolated eigenvalues of the ferromagnetic spin-J XXZ chain with kink boundary conditions. J. Stat. Mech. P01016 (2008) 19 pages. http://front.math.ucdavis.edu/0709.1733
  15. (with Marco Merkli) A resonance theory for open quantum systems with time-dependent dynamics. J. Statist. Phys. 134 (2009) 871--898. http://arxiv.org/abs/0810.3540
  16. (with P. Contucci) Thermodynamic Limit for Spin Glasses. Beyond the Annealed Bound. J. Statist. Phys. 135 (2009) 1159--1166. http://arxiv.org/abs/0809.4229
  17. Thermodynamic Limit for the Mallows Model on $S_n$. J. Math. Phys. 50 (2009) 095208 (15 pages). http://arxiv.org/abs/0904.0696
  18. (with B. Nachtergaele, Benjamin Schlein, R. Sims and Valentin Zagrebnov) On the existence of the dynamics for anharmonic quantum oscillator systems. Rev. Math. Phys. 22 (2010) 207--231. http://arxiv.org/abs/0909.2249
  19. (with Andrew Ledoan and M.~Merkli) A universality property of Gaussian analytic functions. J. Theoret. Probab. accepted and available at Online First. http://arxiv.org/abs/1003.1951
  20. (with Carl Mueller) The length of the longest increasing subsequence of a random Mallows permutation. J. Theoret. Probab. accepted and available at Online First. http://arxiv.org/abs/1102.3402
  21. (with Matt Conomos) Asymptotics of the spectral gap for the interchange process on large hypercubes. J. Statist. Mech. accepted. http://arxiv.org/abs/0802.1368
    Refereed Proceedings Articles (RPA)
  1. (with B. Nachtergaele and W. Spitzer) On the dynamics of interfaces in the ferromagnetic XXZ chain under weak perturbations. In Y.~Karpeshina, G. Stolz, R. Weikard, and Y. Zeng (Eds), Advances in Differential Equations and Mathematical Physics, Contemporary Mathematics, vol 327, American Mathematical Society (2003) pp. 251--270. http://arxiv.org/abs/math-ph/0210017
  2. (with B. Nachtergaele) Ordering of energy levels in Heisenberg models and applications. In Joachim Asch and Alain Joye (Eds.), Mathematical Physics of Quantum Mechanics: Selected and Refereed Lectures from QMath9, Lecture Notes in Physics, Vol 690, Springer-Verlag, 2006. http://arxiv.org/abs/math-ph/0503056
  3. (with M. Aizenman and R. Sims) Mean-Field Spin Glass models from the Cavity-ROSt Perspective. In J. C. Mourao, J. P. Nunes, R. Picken and J.-C. Zambrini (Eds), Prospects in Mathematical Physics, Contemporary Mathematics vol 437, American Mathematical Society (2007) pp. 1--30. http://arxiv.org/abs/math-ph/0607060
  4. Universality of Correlations for Random Analytic Functions. In R. Sims and D. Ueltschi (Eds), Entropy and the Quantum II, Contemporary Mathematics vol 552, American Mathematical Society (2011) pp. 135--144. http://arxiv.org/abs/1107.4135
    Preprints (P)
  1. (with B. Nachtergaele and Stephen Ng) Ferromagnetic Ordering of Energy Levels for $U_q(\mathfrak{sl}_2)$ symmetric spin chains. Preprint, submitted to Letters in Mathematical Physics. http://arxiv.org/abs/1105.5264
  2. (with B. Vermesi) Thinning invariant partition structures. Preprint, submitted to Journal of Statistical Physics. http://arxiv.org/abs/1106.0267
  3. (with Sander Dommers, C. Giardinà and P. Contucci) Antiferromagnetic Potts model on the Erdös-Rényi random graph. {\em Preprint, submitted.} http://arxiv.org/abs/1106.4714
  4. (with W. Spitzer and Lam Tran) Counterexamples to Ferromagnetic Ordering of Energy Levels. Preprint, submitted to Journal of Mathematical Physics. http://arxiv.org/abs/1107.1266
    Articles in Preparation (AIP)
  1. (with Meg Walters) Concentration of the Mallows measure.
  2. (with S. Ng) Dual bases for the graphical representation in $\mathcal{U}_q(\mathfrak{sl}_2)$.