Skip to Main Content

Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

MathSciNet review: 4007386
Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Antonio Auffinger, Michael Damron and Jack Hanson
Title: 50 years of first-passage percolation
Additional book information: University Lecture Series, Vol. 68, American Mathematical Society, Providence, RI, v+161 pp., ISBN 978-1-4704-4183-8

References [Enhancements On Off] (What's this?)

  • Tonći Antunović and Eviatar B. Procaccia, Stationary Eden model on Cayley graphs, Ann. Appl. Probab. 27 (2017), no. 1, 517–549. MR 3619794, DOI 10.1214/16-AAP1210
  • Antonio Auffinger and Michael Damron, Differentiability at the edge of the percolation cone and related results in first-passage percolation, Probab. Theory Related Fields 156 (2013), no. 1-2, 193–227. MR 3055257, DOI 10.1007/s00440-012-0425-4
  • Antonio Auffinger and Michael Damron, A simplified proof of the relation between scaling exponents in first-passage percolation, Ann. Probab. 42 (2014), no. 3, 1197–1211. MR 3189069, DOI 10.1214/13-AOP854
  • Antonio Auffinger, Michael Damron, and Jack Hanson, Rate of convergence of the mean for sub-additive ergodic sequences, Adv. Math. 285 (2015), 138–181. MR 3406498, DOI 10.1016/j.aim.2015.07.028
  • Antonio Auffinger, Michael Damron, and Jack Hanson, 50 years of first-passage percolation, University Lecture Series, vol. 68, American Mathematical Society, Providence, RI, 2017. MR 3729447, DOI 10.1090/ulect/068
  • Itai Benjamini, Gil Kalai, and Oded Schramm, First passage percolation has sublinear distance variance, Ann. Probab. 31 (2003), no. 4, 1970–1978. MR 2016607, DOI 10.1214/aop/1068646373
  • Raphaël Cerf and Marie Théret, Weak shape theorem in first passage percolation with infinite passage times, Ann. Inst. Henri Poincaré Probab. Stat. 52 (2016), no. 3, 1351–1381 (English, with English and French summaries). MR 3531712, DOI 10.1214/15-AIHP686
  • S. Chatterjee, A general method for lower bounds on fluctuations of random variables, arXiv:1706.04290 (2017).
  • J. Theodore Cox and Richard Durrett, Some limit theorems for percolation processes with necessary and sufficient conditions, Ann. Probab. 9 (1981), no. 4, 583–603. MR 624685
  • J. Theodore Cox and Harry Kesten, On the continuity of the time constant of first-passage percolation, J. Appl. Probab. 18 (1981), no. 4, 809–819. MR 633228, DOI 10.1017/s0021900200034161
  • Michael Damron, Jack Hanson, and Philippe Sosoe, Sublinear variance in first-passage percolation for general distributions, Probab. Theory Related Fields 163 (2015), no. 1-2, 223–258. MR 3405617, DOI 10.1007/s00440-014-0591-7
  • Richard Durrett and Thomas M. Liggett, The shape of the limit set in Richardson’s growth model, Ann. Probab. 9 (1981), no. 2, 186–193. MR 606981
  • Murray Eden, A two-dimensional growth process, Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. IV, Univ. California Press, Berkeley, Calif., 1961, pp. 223–239. MR 0136460
  • Dvir Falik and Alex Samorodnitsky, Edge-isoperimetric inequalities and influences, Combin. Probab. Comput. 16 (2007), no. 5, 693–712. MR 2346808, DOI 10.1017/S0963548306008340
  • Olivier Garet, Régine Marchand, Eviatar B. Procaccia, and Marie Théret, Continuity of the time and isoperimetric constants in supercritical percolation, Electron. J. Probab. 22 (2017), Paper No. 78, 35. MR 3710798, DOI 10.1214/17-EJP90
  • J. M. Hammersley and D. J. A. Welsh, First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory, Proc. Internat. Res. Semin., Statist. Lab., Univ. California, Berkeley, Calif., 1963., Springer-Verlag, New York, 1965, pp. 61–110. MR 0198576
  • M. Kardar, G. Parisi, and Y.-C. Zhang, Dynamic scaling of growing interfaces, Phys. Rev. Lett. 56 (Mar 1986), 889–892.
  • Harry Kesten, Aspects of first passage percolation, École d’été de probabilités de Saint-Flour, XIV—1984, Lecture Notes in Math., vol. 1180, Springer, Berlin, 1986, pp. 125–264. MR 876084, DOI 10.1007/BFb0074919
  • Harry Kesten, On the speed of convergence in first-passage percolation, Ann. Appl. Probab. 3 (1993), no. 2, 296–338. MR 1221154
  • J. F. C. Kingman, The ergodic theory of subadditive stochastic processes, J. Roy. Statist. Soc. Ser. B 30 (1968), 499–510. MR 254907
  • J. F. C. Kingman, Subadditive ergodic theory, Ann. Probability 1 (1973), 883–909. MR 356192, DOI 10.1214/aop/1176996798
  • Raz Kupferman, Cy Maor, and Ron Rosenthal, Non-metricity in the continuum limit of randomly-distributed point defects, Israel J. Math. 223 (2018), no. 1, 75–139. MR 3773058, DOI 10.1007/s11856-017-1620-x
  • Thomas M. Liggett, An improved subadditive ergodic theorem, Ann. Probab. 13 (1985), no. 4, 1279–1285. MR 806224
  • R. Marchand, Strict inequalities for the time constant in first passage percolation, Ann. Appl. Probab. 12 (2002), no. 3, 1001–1038. MR 1925450, DOI 10.1214/aoap/1031863179
  • R. W. Morgan and D. J. A. Welsh, A two-dimensional Poisson growth process, J. Roy. Statist. Soc. Ser. B 27 (1965), 497–504. MR 193695
  • Charles M. Newman and Marcelo S. T. Piza, Divergence of shape fluctuations in two dimensions, Ann. Probab. 23 (1995), no. 3, 977–1005. MR 1349159
  • Daniel Richardson, Random growth in a tessellation, Proc. Cambridge Philos. Soc. 74 (1973), 515–528. MR 329079, DOI 10.1017/s0305004100077288
  • John C. Wierman and Wolfgang Reh, On conjectures in first passage percolation theory, Ann. Probability 6 (1978), no. 3, 388–397. MR 478390, DOI 10.1214/aop/1176995525
  • J. G. Zabolitzky and D. Stauffer, Simulation of large eden clusters, Phys. Rev. A 34 (Aug 1986), 1523–1530.

  • Review Information:

    Reviewer: Ron Rosenthal
    Affiliation: Department of Mathematics, Technion—Israel Institute of Technology, Haifa, Israel
    Journal: Bull. Amer. Math. Soc. 56 (2019), 713-720
    Published electronically: August 7, 2018
    Review copyright: © Copyright 2018 American Mathematical Society