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Introduction

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Large Deviations for Random Graphs

Part of the book series: Lecture Notes in Mathematics ((LNMECOLE,volume 2197))

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Abstract

This introductory chapter lays out the general plan of the book and gives a quick description of the main issues.

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References

  1. Aristoff, D., & Radin, C. (2013). Emergent structures in large networks. Journal of Applied Probability, 50(3), 883–888.

    Article  MathSciNet  MATH  Google Scholar 

  2. Bhattacharya, B. B., Ganguly, S., Lubetzky, E., & Zhao, Y. (2015). Upper tails and independence polynomials in random graphs. arXiv preprint arXiv:1507.04074.

    Google Scholar 

  3. Bollobás, B., & Riordan, O. (2009). Metrics for sparse graphs. In Surveys in combinatorics 2009, vol. 365, London Mathematical Society Lecture Note Series (pp. 211–287). Cambridge: Cambridge University Press.

    Google Scholar 

  4. Borgs, C., Chayes, J. T., Cohn, H., & Zhao, Y. (2014). An L p theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions. arXiv preprint arXiv:1401.2906.

    Google Scholar 

  5. Borgs, C., Chayes, J. T., Cohn, H., & Zhao, Y. (2014). An L p theory of sparse graph convergence II: LD convergence, quotients, and right convergence. arXiv preprint arXiv:1408.0744.

    Google Scholar 

  6. Chatterjee, S. (2016). An introduction to large deviations for random graphs. Bulletin of the American Mathematical Society, 53(4), 617–642.

    Article  MathSciNet  MATH  Google Scholar 

  7. Chatterjee, S., & Dembo, A. (2016). Nonlinear large deviations. Advances in Mathematics, 299, 396–450.

    Article  MathSciNet  MATH  Google Scholar 

  8. Chatterjee, S., & Diaconis, P. (2013). Estimating and understanding exponential random graph models. Annals of Statistics, 41(5), 2428–2461.

    Article  MathSciNet  MATH  Google Scholar 

  9. Chatterjee, S., & Varadhan, S. R. S. (2011). The large deviation principle for the Erdős-Rényi random graph. European Journal of Combinatorics, 32(7), 1000–1017.

    Article  MathSciNet  MATH  Google Scholar 

  10. Dembo, A., & Zeitouni, O. (2010). Large deviations techniques and applications. Corrected reprint of the second (1998) edition. Berlin: Springer.

    Google Scholar 

  11. Eldan, R. (2016). Gaussian-width gradient complexity, reverse log-Sobolev inequalities and nonlinear large deviations. arXiv preprint arXiv:1612.04346.

    Google Scholar 

  12. Erdős, P., & Rényi, A. (1960). On the evolution of random graphs. Publication of the Mathematical Institute of the Hungarian Academy of Sciences, 5, 17–61.

    MathSciNet  MATH  Google Scholar 

  13. Kenyon, R., Radin, C., Ren, K., & Sadun, L. (2014). Multipodal structure and phase transitions in large constrained graphs. arXiv preprint arXiv:1405.0599.

    Google Scholar 

  14. Kenyon, R., & Yin, M. (2014). On the asymptotics of constrained exponential random graphs. arXiv preprint arXiv:1406.3662.

    Google Scholar 

  15. Kim, J. H., & Vu, V. H. (2000). Concentration of multivariate polynomials and its applications. Combinatorica, 20(3), 417–434.

    Article  MathSciNet  MATH  Google Scholar 

  16. Latała, R. (1997). Estimation of moments of sums of independent real random variables. The Annals of Probability, 25(3), 1502–1513.

    Article  MathSciNet  MATH  Google Scholar 

  17. Lubetzky, E., & Zhao, Y. (2015). On replica symmetry of large deviations in random graphs. Random Structures Algorithms, 47(1), 109–146.

    Article  MathSciNet  MATH  Google Scholar 

  18. Lubetzky E., & Zhao, Y. (2017). On the variational problem for upper tails of triangle counts in sparse random graphs. Random Structures Algorithms, 50(3), 420–436.

    Article  MathSciNet  MATH  Google Scholar 

  19. Radin, C., & Sadun, L. (2013). Phase transitions in a complex network. Journal of Physics A, 46, 305002.

    Article  MathSciNet  MATH  Google Scholar 

  20. Radin, C., & Yin, M. (2011). Phase transitions in exponential random graphs. arXiv preprint arXiv:1108.0649.

    Google Scholar 

  21. Talagrand, M. (1995). Concentration of measure and isoperimetric inequalities in product spaces. Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 81, 73–205.

    Article  MathSciNet  MATH  Google Scholar 

  22. Vu, V. H. (2002). Concentration of non-Lipschitz functions and applications. Probabilistic methods in combinatorial optimization. Random Structures Algorithms, 20(3), 262–316.

    Article  MathSciNet  MATH  Google Scholar 

  23. Yin, M. (2013). Critical phenomena in exponential random graphs. Journal of Statistical Physics, 153(6), 1008–1021.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, Stanford University, Stanford, CA, USA

    Sourav Chatterjee

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  1. Sourav Chatterjee
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Chatterjee, S. (2017). Introduction. In: Large Deviations for Random Graphs. Lecture Notes in Mathematics(), vol 2197. Springer, Cham. https://doi.org/10.1007/978-3-319-65816-2_1

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