C. Castellano, S. Fortunato and V. Loreto, Statistical Physics of Social Dynamics, Rev. Mod. Phys, 81, 591 (2009) [PDF]
Lecture notes [PDF]
Suggested readings
[PIETRONERO, 2001]: L. Pietronero, E. Tosatti, V. Tosatti, A. Vespignani, “Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf”, Physica A, 293, 297–304 (2001). [PDF] {On the Benford's law}
[NEWMAN, 2005] : Newman, M. E. J., “Power laws, Pareto distributions and Zipf’s law”, Contemporary Physics, 46, 323–351 (2005). [PDF]
{Review of the possible pathways to the emergence of power-laws} [https://arxiv.org/abs/cond-mat/0412004]
[BETTENCOURT, 2007]: L. Bettencourt, J, Lobo‡ D. Helbing, C. Kuhnert, and G.B. West, “Growth, innovation, scaling, and the pace of life in cities”, PNAS, vol. 104(17), 7301–7306 (2007). [PDF]
[WEST, 1997]: Geoffrey B. West, James H. Brown, Brian J. Enquist, “A General Model for the Origin of Allometric Scaling Laws in Biology”, Science, vol. 276, 122-126 (1997). [PDF]
[WILLIS, 1922]: Willis, J.C. and Yule G.U. “Some Statistics of Evolution and Geographical Distribution in Plants and Animals, and their Significance”, Nature, 109(2728), 177–179. (1922). [PDF]
[SIMON, 1955]: H.A. Simon, “A Behavioural Model of Rational Choice”, The Quarterly Journal of Economics, Volume 69(1), 99– 118 (1955) [PDF]
others:
Michael Mitzenmacher, A Brief History of Generative Models for Power Law and Log-normal Distributions, Internet Math. 1, 226 (2003) [PDF]
{Analysis of the possible relationships between log-normal and power-law distributions}
Suggested books:
Lecture Notes [PDF]
Suggested readings
C.E. Shannon, A Mathematical Theory of Communication, Bell Systems Technical Journal, Vol. 27 (1948), pp. 379–423, 623–656. [PDF]
C.E. Shannon, Prediction and Entropy of Printed English, Bell Systems Technical Journal, Vol. 30 (1951), pp. 50-64. [PDF]
A.D. Wyner, Typical sequences and all that: entropy, pattern matching and data compression, 1994 Shannon Lecture [PDF]
T Schurmann e P. Grassberger, Entropy estimation of symbol sequences, Chaos, 6, 50-64 (1996) [PDF]
Suggested books:
Elements of Information Theory. Thomas M. Cover, Joy A. Thomas. Wiley Series in Telecommunications (1991). 2nd Edition (2006).
Information theory, inference and learning algorithms. David J.C. MacKay. Cambridge University Press (2003).
Chaos: From Simple Models to Complex Systems. Cencini, Massimo; Cecconi, Fabio; Vulpiani, Angelo. World Scientific Publishing Co. Pte. Ltd., . ISBN (2010).
Suggested readings:
[N] Mark. Newman: "The Structure and Function of Complex Networks", SIAM Review, Vol. 45(2) (2003) [PDF]
[AB] Réka Albert and Albert Lászlo Bárabási: "Statistical mechanics of complex networks", Rev. Mod. Phys., 74(51) (2002) [PDF]
[EPI] Romualdo Pastor-Satorras, Claudio Castellano, Piet Van Mieghem, Alessandro Vespignani, "Epidemic processes in complex networks", Rev. Mod. Phys., 87(3) (2015) [PDF]
[ER] : Paul Erdős, Alfred Rényi, On random graphs, Publicationes Mathematicae Debrecen 6 (1959), 290–297. [PDF]
Lecture Notes [PDF]
Suggested readings:
The dynamics of correlated novelties
F. Tria, V. Loreto, V. D. P. Servedio & S. H. Strogatz
Scientific Reports volume 4, Article number: 5890 (2014)
https://www.nature.com/articles/srep05890
"Dynamics on Expanding Spaces: Modelling the Emergence of Novelties"
Vittorio Loreto, Vito D. P. Servedio, Steven H. Strogatz & Francesca Tria
Chapter on Lecture Notes in Morphogenesis book series
https://link.springer.com/chapter/10.1007/978-3-319-24403-7_5
https://arxiv.org/pdf/1701.00994.pdf
Lecture Notes (by Claudio Castellano) [PDF]
Suggested readings:
“Statistical Physics of Social Dynamics"
C. Castellano, S. Fortunato and V. Loreto,
Rev. Mod. Phys. 81, 591 (2009)
https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.81.591 [PDF]
“Non-equilibrium phase transition in a model of social influence”
C. Castellano, M. Marsili and A. Vespignani,
Phys. Rev. Lett. 85, 3536 (2000)
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.85.3536 [PDF]
“The dissemination of culture. A model with local convergence and global polarization”
R. Axelrod,
J. Conflict Resolut. 41, 203 (1997).
https://journals.sagepub.com/doi/10.1177/0022002797041002001 [PDF]
"Sharp transition towards shared vocabularies in multi-agent systems"
Andrea Baronchelli, Maddalena Felici, Vittorio Loreto, Emanuele Caglioti and Luc Steels
Journal of Statistical Mechanics: Theory and Experiment, P06014 (2006)
https://iopscience.iop.org/article/10.1088/1742-5468/2006/06/P06014 [PDF]
"Opinion Dynamics with Disagreement and Modulated Information"
Alina Sîrbu, Vittorio Loreto, Vito D. P. Servedio & Francesca Tria
Journal of Statistical Physics volume 151, pages 218–237 (2013)
https://link.springer.com/article/10.1007/s10955-013-0724-x [PDF]