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Abstract
It is customary to date the initial foray of physicists into economics to the September 1987 Santa Fe conference on “Economics as a complex evolving system", organised by two famous physicists (Phil Anderson & David Pines) and one famous economist (Ken Arrow). When confronted with the theories of Rational Expectations and Efficient Markets, then at the peak of their glory, Phil Anderson famously quipped: Do you guys really believe that? Many inspiring and insightful ideas were discussed during that conference [1], suggesting a potentially productive cross-fertilisation between economics and the (back then) nascent theory of complex systems.
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Bun J, Bouchaud JP, Majumdar SN, Potters M. Instanton approach to large N Harish-Chandra-Itzykson-Zuber integrals. Phys Rev Lett 2014; 113:070201. [PMID: 25170689 DOI: 10.1103/physrevlett.113.070201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2014] [Indexed: 06/03/2023]
Abstract
We reconsider the large N asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary case. Our method is easily generalized to the orthogonal and symplectic ensembles. We obtain an explicit solution of Matytsin's equations in the case of Wigner matrices, as well as a general expansion method in the dilute limit, when the spectrum of eigenvalues spreads over very wide regions.
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Affiliation(s)
- J Bun
- Capital Fund Management, 23-25, rue de l'Université, 75007 Paris, France and CNRS, LPTMS, Batiment 100, Université d'Orsay, 91405 Orsay Cedex, France and DeVinci Finance Lab, Pôle Universitaire Léonard de Vinci, 92916 Paris La Défense, France
| | - J P Bouchaud
- Capital Fund Management, 23-25, rue de l'Université, 75007 Paris, France
| | - S N Majumdar
- CNRS, LPTMS, Batiment 100, Université d'Orsay, 91405 Orsay Cedex, France
| | - M Potters
- Capital Fund Management, 23-25, rue de l'Université, 75007 Paris, France
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Affiliation(s)
- E. Vincent
- a Service de Physique de l'Etat Condensé, Commissariat à l'Energie Atomique Saclay , 91191 , Gif-Sur-Yvette, France
| | - J. P. Bouchaud
- a Service de Physique de l'Etat Condensé, Commissariat à l'Energie Atomique Saclay , 91191 , Gif-Sur-Yvette, France
| | - J. Hammann
- a Service de Physique de l'Etat Condensé, Commissariat à l'Energie Atomique Saclay , 91191 , Gif-Sur-Yvette, France
| | - F. Lefloch
- a Service de Physique de l'Etat Condensé, Commissariat à l'Energie Atomique Saclay , 91191 , Gif-Sur-Yvette, France
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Bonamy D, Daviaud F, Laurent L, Bonetti M, Bouchaud JP. Multiscale clustering in granular surface flows. Phys Rev Lett 2002; 89:034301. [PMID: 12144395 DOI: 10.1103/physrevlett.89.034301] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2001] [Indexed: 05/23/2023]
Abstract
We investigate steady granular surface flows in a rotating drum and demonstrate the existence of rigid clusters of grains embedded in the flowing layer. These clusters appear to be fractal and their size is power law distributed from the grain size scale up to the thickness of the flowing layer. The implications of the absence of a characteristic length scale on available theoretical models of dense granular flows are discussed. Finally, we suggest a possible explanation of the difference between velocity profiles observed in surface flows and in flows down a rough inclined plane.
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Affiliation(s)
- D Bonamy
- Service de Physique de l'Etat Condensé, CEA/DSM Saclay, 91191 Gif sur Yvette, France
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Abstract
We investigate quantitatively the so-called "leverage effect," which corresponds to a negative correlation between past returns and future volatility. For individual stocks this correlation is moderate and decays over 50 days, while for stock indices it is much stronger but decays faster. For individual stocks the magnitude of this correlation has a universal value that can be rationalized in terms of a new "retarded" model which interpolates between a purely additive and a purely multiplicative stochastic process. For stock indices a specific amplification phenomenon seems to be necessary to account for the observed amplitude of the effect.
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Affiliation(s)
- J P Bouchaud
- Service de Physique de l'Etat Condensé, Centre d'études de Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France
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Abstract
We investigate aging in glassy systems based on a simple model, where a point in configuration space performs thermally activated jumps between the minima of a random energy landscape. The model allows us to show explicitly a subaging behavior and multiple scaling regimes for the correlation function. Both the exponents characterizing the scaling of the different relaxation times with the waiting time and those characterizing the asymptotic decay of the scaling functions are obtained analytically by invoking a "partial equilibrium" concept.
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Affiliation(s)
- B Rinn
- Fakultat fur Physik, Universitat Konstanz, D-78457 Konstanz, Germany
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Bouchaud JP, Mézard M. Velocity fluctuations in forced Burgers turbulence. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1996; 54:5116-5121. [PMID: 9965691 DOI: 10.1103/physreve.54.5116] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Bouchaud JP, Mézard M, Parisi G. Scaling and intermittency in Burgers turbulence. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1995; 52:3656-3674. [PMID: 9963845 DOI: 10.1103/physreve.52.3656] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Vincent E, Bouchaud JP, Dean DS, Hammann J. Aging in spin glasses as a random walk: Effect of a magnetic field. Phys Rev B Condens Matter 1995; 52:1050-1060. [PMID: 9980682 DOI: 10.1103/physrevb.52.1050] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Moore MA, Blum T, Doherty JP, Marsili M, Bouchaud JP, Claudin P. Glassy solutions of the Kardar-Parisi-Zhang equation. Phys Rev Lett 1995; 74:4257-4260. [PMID: 10058455 DOI: 10.1103/physrevlett.74.4257] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Bouchaud JP, Vincent E, Hammann J. Towards an experimental determination of the number of metastable
states in spin-glasses? ACTA ACUST UNITED AC 1994. [DOI: 10.1051/jp1:1994127] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Bouchaud JP, Cates ME. Erratum: Self-consistent approach to the Kardar-Parisi-Zhang equation. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1993; 48:635-636. [PMID: 9960634 DOI: 10.1103/physreve.48.635.2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Bouchaud JP, Cates ME. Self-consistent approach to the Kardar-Parisi-Zhang equation. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1993; 47:R1455-R1458. [PMID: 9960250 DOI: 10.1103/physreve.47.r1455] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Bouchaud JP, Mézard M, Yedidia JS. Variational theory for the pinning of vortex lattices by impurities. Phys Rev B Condens Matter 1992; 46:14686-14701. [PMID: 10003570 DOI: 10.1103/physrevb.46.14686] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bouchaud JP, Georges A. Competition between lattice pinning and impurity pinning: Variational theory and physical realizations. Phys Rev Lett 1992; 68:3908-3911. [PMID: 10045835 DOI: 10.1103/physrevlett.68.3908] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Krauth W, Caffarel M, Bouchaud JP. Gutzwiller wave function for a model of strongly interacting bosons. Phys Rev B Condens Matter 1992; 45:3137-3140. [PMID: 10001873 DOI: 10.1103/physrevb.45.3137] [Citation(s) in RCA: 134] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bouchaud JP, Ott A, Langevin D, Urbach W. Anomalous diffusion in elongated micelles and its Lévy flight interpretation. ACTA ACUST UNITED AC 1991. [DOI: 10.1051/jp2:1991163] [Citation(s) in RCA: 47] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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Ott A, Bouchaud JP, Langevin D, Urbach W. Anomalous diffusion in "living polymers": A genuine Levy flight? Phys Rev Lett 1990; 65:2201-2204. [PMID: 10042479 DOI: 10.1103/physrevlett.65.2201] [Citation(s) in RCA: 66] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Bouchaud JP, Georges A. Comment on "Diffusion and drift of charge carriers in a random potential: Deviation from Einstein's law". Phys Rev Lett 1989; 63:2692. [PMID: 10040962 DOI: 10.1103/physrevlett.63.2692] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Bouchaud JP, Zérah PG. Spontaneous resonances and universal behavior in ferrimagnets: Effective-medium theory. Phys Rev Lett 1989; 63:1000-1003. [PMID: 10041243 DOI: 10.1103/physrevlett.63.1000] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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