Fetching the paper…
Reading the bibliography…
In this article we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos.
L. Onsager: Electrostatic interaction between molecules. J. Phys. Chem. 43 (1939), 189–196
1939
Earlier work this paper cites.
B. von Bahr, and C.-G. Esseen: Inequalities for the r r :th absolute moment of a sum of random variables, 1 ≤ r ≤ 2 1\leq r\leq 2 . Ann. Math. Statist 36, 1965, 299–303
1965
Earlier work this paper cites.
E. Stein and G. Weiss: Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, 1971
1971
Earlier work this paper cites.
J.-P. Kahane: Sur le chaos multiplicatif. Ann. Sci. Math. Québec 9(2), 105–150 (1985)
1985
Earlier work this paper cites.
O. Blasco: Boundary values of functions in vector-valued Hardy spaces and geometry on Banach spaces. J. Funct. Anal. 78 (2) (1988), 346–364
1988
Earlier work this paper cites.
E. B. Davies: Lipschitz continuity of functions of operators in the Schatten classes. J. London Math. Soc. (2) 37 (1988), no. 1, 148–157
1988
Earlier work this paper cites.
H. Triebel: Interpolation theory, function spaces, differential operators. Second edition. Johann Ambrosius Barth, Heidelberg, 1995
1995
Earlier work this paper cites.
J. Barral: Techniques for the study of infinite products of independent random functions (Random multiplicative multifractal measures. III), in Fractal geometry and applications: a jubilee of Benoit Mandelbrot, Part 2, pp. 53–90. Proc. Sympos. Pure Math., 72, Part 2, Amer. Math. Soc., Providence, RI, 2004
2004
Earlier work this paper cites.
Bogachev V. I., Measure theory. Vol. I, II, Springer-Verlag, Berlin, 2007
2007
Earlier work this paper cites.
S. Sheffield: Gaussian free fields for mathematicians. Probab. Theory Related Fields 139 (2007), no. 3–4, 521–541
2007
Earlier work this paper cites.
R. J. Adler, and J. E. Taylor: Random fields and geometry. Springer Science & Business Media, 2009
2009
Earlier work this paper cites.
J. Barral, X. Jin, and B. Mandelbrot: Uniform convergence for complex [ 0 , 1 ] [0,1] -martingales. Ann. Appl. Probab., 2010, vol. 20, no 4, 1205–1218
2010
Earlier work this paper cites.
K. Astala, P. Jones, A. Kupiainen, and E. Saksman: Random conformal weldings. Acta Math. 207 (2011), no. 2, 203–254
2011
Cited alongside, same era.
B. Duplantier and S. Sheffield: Liouville quantum gravity and KPZ. Invent. Math. 185 (2011), no. 2, 333–393
2011
Cited alongside, same era.
B. Duplantier and S. Sheffield: Schramm–Loewner Evolution and Liouville Quantum Gravity. Phys. Rev. Lett. 107 (2011), 131–305
2011
Cited alongside, same era.
D. Potapov and F. Sukochev: Operator-Lipscitz functions on Schatten-von Neumann classes. Acta Math 207 (2011), 375–389
2011
Cited alongside, same era.
J. Barral, R. Rhodes, and V. Vargas: Limiting laws of supercritical branching random walks. C. R. Math. Acad. Sci. Paris 350 (2012), no. 9-10, 535–538
2012
Cited alongside, same era.
T. Hytönen, J. van Neerven, M. Veraar, L. Weis: Analysis in Banach spaces. Vol. I. Martingales and Littlewood–Paley theory. Springer, Cham, 2016
2016
Later among the works it cites.
T. Madaule, R. Rhodes, and V. Vargas: Glassy phase and freezing of log-correlated Gaussian potentials. Ann. Appl. Prob. 26(2) (2016), 643–690
2016
Later among the works it cites.
A. Shamov: On Gaussian multiplicative chaos. J. Funct. Anal. 270 (2016), 3224–3261
2016
Later among the works it cites.
S. Sheffield: Conformal weldings of random surfaces: SLE and the quantum gravity zipper. Ann. Probab. 44(5), 3474–3545 (2016)
2016
Later among the works it cites.
N. Berestycki: An elementary approach to Gaussian multiplicative chaos. Electron. Commun. Probab. 22 (2017), Paper No. 27, 12 pp
2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
B. Duplantier, R. Rhodes, S. Sheffield, and V.Vargas: Critical Gaussian multiplicative chaos: convergence of the derivative martingale, Ann. Probab. 42(5) (2014), 1769–1808
2014
Cited alongside, same era.
B. Duplantier, R. Rhodes, S. Sheffield, and V.Vargas: Renormalization of critical Gaussian multiplicative chaos and KPZ relation, Comm. Math. Phys. 330(1) (2014), 283–330
2014
Cited alongside, same era.
R. Rhodes and V. Vargas: Gaussian multiplicative chaos and applications: a review. Probab. Surv. 11 (2014), 315–392
2014
Cited alongside, same era.
H. Lacoin, R. Rhodes, and V. Vargas: Complex gaussian multiplicative chaos. Comm. Math. Phys. 337 (2015), 569–632
2015
Cited alongside, same era.
T. Madaule: Maximum of a log-correlated Gaussian field. Ann. Inst. Henri Poincaré Probab. Stat. 51 (2015), no. 4, 1369–1431
2015
Cited alongside, same era.
C. Webb: The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos—the L 2 L^{2} -phase. Electron. J. Probab. 20 (2015), no. 104, 21 pp
2015
Cited alongside, same era.
F. David, A. Kupiainen, R. Rhodes, and V. Vargas: Liouville Quantum Gravity on the Riemann sphere. Commun. Math. Phys. 342 (3) (2016), 869–907
2016
Cited alongside, same era.
N. Berestycki, C. Webb, and M.D. Wong: Random Hermitian Matrices and Gaussian Multiplicative Chaos. Probab. Theory Related Fields 172 (2017), no. 1–2, 103-189
2017
Later among the works it cites.
J. Junnila and E. Saksman: Uniqueness of critical Gaussian chaos. Electron. J. Probab. 22 (2017), no. 11, 31 pp
2017
Later among the works it cites.
J. Najnudel: On the extreme values of the Riemann zeta function on random intervals of the critical line. Probab. Theory Related Fields 172 (2017), no. 1–2, 387–452
2017
Later among the works it cites.
R. Chhaibi, T. Madaule, and J. Najnudel: On the maximum of the C β \beta E field. Duke Math. J. 167, no. 12 (2018), 2243-2345
2018
Closest in time.
G. Lambert, D. Ostrovsky, and N. Simm: Subcritical Multiplicative Chaos for Regularized Counting Statistics from Random Matrix Theory. Commun. Math. Phys. (2018). Comm. Math. Phys. 360 (2018), no. 1, 1–54
2018
Closest in time.
E. Powell: Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation. Electron. J. Probab. 23 (2018) no. 31, 26 pp
2018
Closest in time.