Amir Dembo's home page

Address: Department of Statistics and Department of Mathematics,
Stanford University, Stanford, CA 94305.
Phone: (650) 7252237.
Fax: (650) 7258977.
e-mail: amir at math.stanford.edu

Areas of interest:

I have neither internships nor RA positions for anyone other than Stanford mathematics or statistics (incoming) PhDs. No reply provided for any request of this type.

Due to time limitation, regardless of the candidate's strength, I do not provide promotion/hiring/tenure evaluations for anyone other than current or past students, post-docs or co-authors of mine.

Because of my influence on many manuscripts in the capacity of PTRF editor, I do not take on refereeing papers for other journals.

Currently teaching: Random walks, networks and environment.

For the most recent correction sheet for the book "Large deviations techniques and applications, second edition" (Springer, Application of Mathematics, vol. 38, 1998) see corrections to hard-cover edition, or to purchase the soft-cover edition.

See my St. Flour summer school lecture notes on Favorite points, cover times and fractals.

Current PhD students: Nike Sun, Anirban Basak, Li-cheng Tsai, Ruojun Huang.

Former PhD students: Andrew Nobel, Tim Zajic, Ioannis Kontoyiannis, Tiefeng Jiang, Yevgeniy Kovchegov, Scott Sheffield, Johan Lim, Dimitris Cheliotis, Olivier Daviaud, Manuel Zamfir, Kamil Szczegot, Jason Miller, Mykhaylo Shkolnikov.

Courses I have recently taught: Discrete probabilistic methods, Introduction to Probability theory, Large deviations, Probability theory, Part II, Probability, limit theorems I (NYU), Probability theory, Part III, The spectrum of large random matrices, Stochastic processes on graphs, Stochastic processes, Probabilistic concepts in statistical physics and information theory, Probability theory, Part I, Advanced Topics in Probability Theory, Introduction to Financial Mathematics, Probability Theory: An Analytic View, Gibbs measures and Introduction to Stochastic Processes.

Publications since 2001: (for complete list, see Vitae).

  1. Dembo, A. and Kontoyiannis, I. Critical behavior in lossy source coding. IEEE IT, 47 (2001), pp. 1230-1237.
  2. Dembo, A., Kagan, A., Shepp, L. Remarks on the maximum correlation coefficient. Bernoulli, 7 (2001), pp. 343-350.
  3. Dembo, A., Gandolfi, A., Kesten, H. Greedy lattice animals: negative values and unconstrained maxima. Ann. Probab. 29 (2001), pp. 205-241.
  4. Dembo, A., Peres, Y., Rosen, J. and Zeitouni, O. Thick Points for Planar Brownian Motion and the Erd\"os-Taylor Conjecture on Random Walk. Acta Math. 186 (2001), pp. 239-270. See also Thick points (Red: at least 30 visits in half a million steps of planar simple random walk, produced by Raissa D'Souza).
  5. Ben Arous, G., Dembo, A., Guionnet, A. Aging of spherical spin glasses. Prob. Th. Rel. Field. 120 (2001), pp. 1-67.
  6. Comets, F. and Dembo, A. Ordered overlaps in disordered mean-field models. Prob. Th. Rel. Field. 121 (2001), pp. 1-29.
  7. Dembo, A., Gantert, N., Peres, Y., Zeitouni, O. Large deviations for random walks on Galton-Watson trees: averaging and uncertainty. Prob. Th. Rel. Field. 122 (2002), pp. 241-288.
  8. Dembo, A., Poonen, B., Shao, Q., Zeitouni, O. Random polynomials having few or no real zeros. J. Amer. Math. Soc. 15 (2002), pp. 857-892.
  9. Dembo, A. and Kontoyiannis, I. Source coding, large deviations and approximate pattern matching. Invited paper, IEEE Trans. IT. 48 (2002), pp. 1590-1615.
  10. Dembo, A., Peres, Y., Rosen, J. and Zeitouni, O. Thick points for intersections of planar sample paths. Trans. Amer. Math. Soc. 354 (2002), pp. 4969-5003.
  11. Dembo, A., Guionnet, A. and Zeitouni, O. Aging properties of Sinai's model of random walk in random environment. In St. Flour summer school 2001 lecture notes by O. Zeitouni.
  12. Dembo, A., Peres, Y. and Rosen, J. Brownian Motion on compact manifolds: cover time and late points. Elect. J. Probab. 8 (2003), 15, pp. 1--14.
  13. Dembo, A., Guionnet, A. and Zeitouni, O. Moderate deviations for the spectral measure of certain random matrices. Ann. Inst. H. Poinc., Probab. and Stat. 39 (2003), pp. 1013-1042.
  14. Dembo, A. and Weissman, T. The minimax distortion redundancy in noisy source coding. IEEE Trans. IT, 49 (2003), pp. 3020-3030.
  15. Dembo, A., Deuschel, J.D. and Duffie, D. Large portfolio losses. Finance and Stochastics, 8 (2004), pp. 3-16.
  16. Dembo, A., Gantert, N. and Zeitouni, O. Large deviations for random walks in random environment with holding times. Ann. Probab., 32 (2004), pp. 996-1029.
  17. Dembo, A., Peres, Y., Rosen, J. and Zeitouni, O. Cover times for Brownian motion and random walks in two dimensions. Ann. Math., 160 (2004), pp. 433-464. See Late points (Yellow: points last visited by a simple random walk on 512x512 torus, produced by Raissa D'Souza).
  18. Bryc, W., Dembo, A. and Kagan, A. On the maximum correlation coefficient. Theory Probab. and Appl. 49 (2004), pp. 191-197.
  19. Dembo, A., Morters, P. and Sheffied, S. Large deviations of Markov chains indexed by random trees. Ann. Inst. H. Poinc., Probab. and Stat. 41 (2005), pp. 971-996.
  20. Dembo, A. and Weissman, T. Universal denoising for the finite-input-general-output channel. IEEE Trans. IT, 51 (2005), pp. 1507-1517.
  21. Dembo, A., Peres, Y., Rosen, J. and Zeitouni, O. Late points for random walks in two dimensions. Ann. Probab. 34 (2006), pp. 219-263.
  22. Bryc, W., Dembo, A. and Jiang, T. Spectral measure of large random Hankel, Markov and Toeplitz matrices. Ann. Probab. 34 (2006), pp. 1-38. Also expanded version (posted on arXiv).
  23. Dembo, A. and Sznitman, A.S. On the disconnection of a discrete cylinder by a random walk. Prob. Th. Rel. Fields 136 (2006), pp. 321-340.
  24. Dembo, A. Simple random covering, disconnection, late and favorite points. Proceedings of the International Congress of Mathematicians, Madrid (2006), Volume III, pp. 535-558. Or expanded version.
  25. Ben Arous, G., Dembo, A. and Guionnet, A. Cugliandolo-Kurchan equations for dynamics of spin-glasses. Prob. Th. Rel. Fields 136 (2006), pp. 619-660.
  26. Dembo, A. and Shao, Q. Large and moderate deviations for Hotelling's T-squared statistic. Elect. Comm. Probab. 11 (2006), pp. 149-159.
  27. Dembo, A., Gantert, N., Peres, Y. and Shi, Z. Valleys and the maximum local time for random walk in random environment. Prob. Th. Rel. Fields 137 (2007), pp. 443-474.
  28. Dembo, A., Peres, Y. and Rosen, J. How large a disc is covered by a random walk in n steps?. Ann. Probab. 35 (2007), pp. 577-601.
  29. Dembo, A. and Deuschel, J.D. Aging for interacting diffusion processes. Ann. Inst. H. Poinc., Probab. and Stat. 43 (2007), pp. 461-480.
  30. Dembo, A., Guionnet, A. and Mazza, C. Limiting dynamics for spherical models of spin glasses at high temperature. J. Stat. Phys. 126 (2007), pp. 781-816.
  31. Dembo, A. and Montanari, A. Finite size scaling for the core of large random hypergraphs. Ann. Appl. Probab. 18 (2008), pp. 1993-2040 ( PDF ).
  32. Dembo, A. and Sznitman, A.S. A lower bound on the disconnection time of a discrete cylinder. In Progress in Probability, vol. 60 (in and out of Equilibrium 2), Birkhauser (2008), pp. 211-227.
  33. Belinschi, S., Dembo, A. and Guionnet A. Spectral measure of heavy tailed band and covariance random matrices. Comm. Math. Phys. 289 (2009), pp. 1023-1055.
  34. Dembo, A. and Montanari, A. Ising models on locally tree-like graphs. Ann. Appl. Probab. 20 (2010), pp. 565-592.
  35. Dembo, A. and Deuschel, J.D. Markovian perturbation, response and fluctuation dissipation theorem. Ann. Inst. Henri Poinc. 46 (2010), pp. 822-852.
  36. Dembo A. and Montanari A. Gibbs measures and phase transitions on sparse random graphs. Brazilian J. of Probab. and Stat. 24 (2010), pp. 137-211. Also expanded version (with Section 1.3 and Section 6; posted on arXiv).
  37. Dembo A. and Sun N. Central limit theorem for biased random walk on multi-type Galton-Watson trees. Elect. J. Probab. 17 (2012), article 75.
  38. Dembo, A. Ding, J. and Gao, F. Persistence of iterated partial sums. Ann. Inst. Henri Poinc. 49 (2013) [sharpening earlier version by Dembo, A. and Gao, F.].
  39. Dembo, A., Montanari, A. and Sun, N. Factor models on locally tree-like graphs. Ann. Probab. 41 (2013), pp. 4162-4213.
  40. Basak, A. and Dembo, A. Limiting spectral distribution of sum of unitary and orthogonal matrices. Elec. Comm. Probab. (2013), article 69.
  41. Dembo, A., Montanari, A., Sly, A. and Sun, N. The replica symmetric solution for Potts models on d-regular graphs. Comm. Math. Phys. 327 (2014), pp. 551-575.
  42. Dembo, A. and Mukherjee, S. No zero-crossings for random polynomials and the heat equation. To appear, Ann. Probab. (2014).
  43. Dembo, A., Shkolnikov, M., Varadhan, S.R.S and Zeitouni, O. Large deviations for diffusions interacting through their ranks. To appear, Comm. Pure Appl. Math. (2014).
  44. Basak, A. and Dembo, A. Ferromagnetic Ising measures on large locally tree-like graphs. Submitted.
  45. Chatterjee, S., Dembo, A. and Ding, J. On level sets of Gaussian fields. Submitted.
  46. Dembo, A. and Tsai, L-C. Weakly asymmetric non-simple exclusion process and the Kardar-Parisi-Zhang equation. Submitted.
  47. Dembo, A., Ding, J., Miller, J. and Peres, Y. Cut-off for lamplighter chanis on tori: dimension interpolation and phase transition. Submitted.
  48. Dembo, A., Huang, R. and Sidoravicius, V. Walking within growing domains: recurrence versus transience. Submitted.
  49. Chatterjee, S. and Dembo, A. Nonlinear large deviations. Submitted.
  50. Dembo, A. and Guo, X. The Patched Brownian motion distribution. Unpublished.
  51. Dembo, A. and Peligrad, M. Moderate deviations for the blockwise bootstrap of dependent data. Unpublished.
  52. Bolthausen, E., Comets, F. and Dembo, A. Large deviations for random matrices and random graphs. Unpublished.

To be posted in the future:

  • Dembo, A. and Ding, J. Persistence probabilities for auto-regressive sequences.
  • Dembo, A., Guionnet, A. and Maurel-Segala, E. Low temperature expansion for matrix models.
  • Dembo, A. and Zamfir, M. Analysis of nonlinear integro-differential equation for aging in mixed p-spin models.
  • Dembo, A. and Montanari, A. Bethe states for graphical models.