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References[Adl10] R. J. Adler. The geometry of random fields. Society for Industrial and Applied Mathematics, 2010. MR3396215 [AT07] R. J. Adler and J. E. Taylor. Random fields and geometry, volume 115. Springer, 2007. MR2319516 [Bas98] R. F. Bass. Diffusions and elliptic operators. Springer, 1998. MR1483890 [BGR61] R. Blumenthal, R. Getoor, and D. Ray. On the distribution of first hits for the symmetric stable processes. Transactions of the American Mathematical Society, 99(3):540–554, 1961. MR0126885 [BGW83] R. Bhattacharya, V. K. Gupta, and E. Waymire. The hurst effect under trends. Journal of Applied Probability, pages 649–662, 1983. MR0713513 [Bil99] P. Billingsley. Convergence of Probability Measures, Wiley Series in Probability and Statistics. Wiley, New York, 1999. MR1700749 [Cap00] P. Caputo. Harmonic Crystals: Statistical Mechanics and Large Deviations. PhD thesis, TU Berlin 2000, http://edocs.tu-berlin.de/diss/index.html, 2000. [CD09] J.-P. Chiles and P. Delfiner. Geostatistics: modeling spatial uncertainty, volume 497. John Wiley & Sons, 2009. MR2850475 [CDDS11] A. Capella, J. Dávila, L. Dupaigne, and Y. Sire. Regularity of radial extremal solutions for some non-local semilinear equations. Communications in Partial Differential Equations, 36(8):1353–1384, 2011. MR2825595 [CG11] S.-Y. A. Chang and M. d. M. González. Fractional Laplacian in conformal geometry. Advances in Mathematics, 226(2):1410–1432, 2011. MR2737789 [CI13] S. Cohen and J. Istas. Fractional fields and applications, volume 73. Springer, 2013. MR3088856 [CS98] Z.-Q. Chen and R. Song. Estimates on Green functions and Poisson kernels for symmetric stable processes. Mathematische Annalen, 312(3):465–501, 1998. MR1654824 [CS07] L. Caffarelli and L. Silvestre. An extension problem related to the fractional Laplacian. Communications in Partial Differential Equations, 32(8):1245–1260, 2007. MR2354493 [CSS08] L. A. Caffarelli, S. Salsa, and L. Silvestre. Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Inventiones Mathematicae, 171(2):425–461, 2008. MR2367025 [CT10] X. Cabré and J. Tan. Positive solutions of nonlinear problems involving the square root of the Laplacian. Advances in Mathematics, 224(5):2052–2093, 2010. MR2646117 [DNPV] E. Di Nezza, G. Palatucci, and E. Valdinoci. Hitchhiker’s guide to the fractional Sobolev spaces. arXiv preprint arxiv:1104.4345. [Dob79] R. Dobrushin. Gaussian and their subordinated self-similar random generalized fields. The Annals of Probability, 1–28, 1979. MR0515810 [Dod03] S. Dodelson. Modern cosmology. Amsterdam (Netherlands): Academic Press, 2003. [DRSV] B. Duplantier, R. Rhodes, S. Sheffield, and V. Vargas. Log-correlated Gaussian field: an overview. In preparation. [DS11] B. Duplantier and S. Sheffield. Liouville quantum gravity and KPZ. Inventiones Mathematicae, 185(2):333–393, 2011. MR2819163 [Dub09] J. Dubédat. SLE and the free field: partition functions and couplings. Journal of the American Mathematical Society, 22(4):995–1054, 2009. MR2525778 [Dud02] R. M. Dudley. Real analysis and probability, volume 74. Cambridge University Press, 2002. MR1932358 [dW51] H. de Wijs. Statistics of ore distribution. part i: frequency distribution of assay values. Journal of the Royal Netherlands Geological and Mining Society, 13:365–375, 1951. [dW53] H. de Wijs. Statistics of ore distribution. part ii: theory of binomial distribution applied to sampling and engineering problems. Journal of the Royal Netherlands Geological and Mining Society, 15:125–24, 1953. [Dyn80] E. Dynkin. Markov processes and random fields. Bulletin of the American Mathematical Society, 3(3):975–999, 1980. MR0585179 [FJ98] G. Friedlander and M. Joshi. Introduction to the theory of distributions. Cambridge University Press, Cambridge, 1998. MR1721032 [Fol99] G. B. Folland. Real analysis: modern techniques and their applications, volume 361. Wiley, New York, 1999. MR1681462 [Gan67] R. Gangolli. Positive definite kernels on homogeneous spaces and certain stochastic processes related to Lévy’s Brownian motion of several parameters. Ann. Inst. H. Poincaré Sect. B (N.S.), 3:121–226, 1967. MR0215331 [GGS10] F. Gazzola, H.-C. Grunau, and G. Sweers. Polyharmonic boundary value problems: positivity preserving and nonlinear higher order elliptic equations in bounded domains. Number 1991. Springer, 2010. MR2667016 [Hör03] L. Hörmander. The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis. Reprint of the second (1990) edition. Springer, Berlin, 2003. [Jan97] S. Janson. Gaussian Hilbert spaces, volume 129. Cambridge University Press, 1997. MR1474726 [Ken01] R. Kenyon. Dominos and the Gaussian free field. Annals of Probability, 1128–1137, 2001. MR1872739 [Kol40] A. N. Kolmogorov. Wienersche spiralen und einige andere interessante kurven im hilbertschen raum. In CR (Dokl.) Acad. Sci. URSS, volume 26, pages 115–118, 1940. MR0003441 [Kri10] G. Kristensson. Second order differential equations: special functions and their classification. Springer, 2010. MR2682403 [Kuo96] H.-H. Kuo. White noise distribution theory. CRC Press, 1996. MR1387829 [Kur07] N. Kurt. Entropic repulsion for a class of Gaussian interface models in high dimensions. Stochastic Processes and Their Applications, 117(1):23–34, 2007. MR2287101 [Kur09] N. Kurt. Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension. The Annals of Probability, 37(2):687–725, 2009. MR2510021 [Lax02] P. D. Lax. Functional analysis. John Wiley und Sons, 2002. MR1892228 [LD72] N. S. Landkof and A. P. Doohovskoy. Foundations of modern potential theory. Springer-Verlag, Berlin, 1972. MR0350027 [Lév40] M. P. Lévy. Le mouvement Brownien plan. American Journal of Mathematics, 62(1):487–550, 1940. MR0002734 [Lév45] P. Lévy. Sur le mouvement Brownien dépendant de plusieurs paramètres. CR Acad. Sci. Paris, 220(420):3–1, 1945. [Man75] B. B. Mandelbrot. On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars. Journal of Fluid Mechanics, 72(03):401–416, 1975. [MC06] P. McCullagh and D. Clifford. Evidence for conformal invariance of crop yields. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 462(2071):2119–2143, 2006. [McC02] P. McCullagh. What is a statistical model? Annals of Statistics, 1225–1267, 2002. MR1936320 [McK63] H. McKean, Jr. Brownian motion with a several-dimensional time. Theory of Probability & Its Applications, 8(4):335–354, 1963. MR0157407 [MO69] S. A. Molchanov and E. Ostrovskii. Symmetric stable processes as traces of degenerate diffusion processes. Theory of Probability & Its Applications, 14(1):128–131, 1969. MR0247668 [Mon15] D. Mondal. Applying Dynkin’s isomorphism: an alternative approach to understand the Markov property of the de wijs process. Bernoulli, 2015. MR3352044 [MP10] P. Mörters and Y. Peres. Brownian motion, volume 30. Cambridge University Press, 2010. MR2604525 [MS] J. Miller and S. Sheffield. Imaginary geometry III: reversibility of SLEκ for κ ∈ (4,8). 2012. arXiv preprint arXiv:1201.1498. [MS12a] J. Miller and S. Sheffield. Imaginary geometry I: interacting SLEs. arXiv preprint arXiv:1201.1496, 2012. [MS12b] J. Miller and S. Sheffield. Imaginary geometry II: reversibility of SLEκ(ρ1,ρ2) for κ ∈ (0,4). arXiv preprint arXiv:1201.1497, 2012. [MS13] J. Miller and S. Sheffield. Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees. arXiv preprint arXiv:1302.4738, 2013. [Mun99] J. Munkres. Topology, 2nd edition. Prentice Hall, 1999. [MVN68] B. B. Mandelbrot and J. W. Van Ness. Fractional Brownian motions, fractional noises and applications. SIAM Review, 10(4):422–437, 1968. MR0242239 [MZ13] I. Melbourne and R. Zweimüller. Weak convergence to stable Lévy processes for nonuniformly hyperbolic dynamical systems. arXiv preprint arXiv:1309.6429, 2013. [New80] C. Newman. Self-similar random fields in mathematical physics. In Proceedings Measure Theory Conference. DeKalb, Illinois, 1980. [Olv10] F. W. Olver. NIST handbook of mathematical functions. Cambridge University Press, 2010. MR2723248 [OW89] M. Ossiander and E. C. Waymire. Certain positive-definite kernels. Proceedings of the American Mathematical Society, 107(2):487–492, 1989. MR1011824 [RV06] B. Rider and B. Virág. The noise in the circular law and the Gaussian free field. arXiv preprint arXiv:math/0606663, 2006. MR2361453 [RV13] R. Rhodes and V. Vargas. Gaussian multiplicative chaos and applications: a review. arXiv preprint arXiv:1305.6221, 2013. MR3274356 [RY99] D. Revuz and M. Yor. Continuous martingales and Brownian motion, volume 293. Springer Verlag, 1999. MR1725357 [Sak03] H. Sakagawa. Entropic repulsion for a Gaussian lattice field with certain finite range interaction. Journal of Mathematical Physics, 44:2939, 2003. MR1982781 [Sak12] H. Sakagawa. On the free energy of a Gaussian membrane model with external potentials. Journal of Statistical Physics, 147(1):18–34, 2012. MR2922757 [She07] S. Sheffield. Gaussian free fields for mathematicians. Probability Theory and Related Fields, 139(3-4):521–541, 2007. MR2322706 [She10] S. Sheffield. Conformal weldings of random surfaces: SLE and the quantum gravity zipper. arXiv preprint arXiv:1012.4797, 2010. MR2251117 [Sil07] L. Silvestre. Regularity of the obstacle problem for a fractional power of the Laplace operator. Communications on Pure and Applied Mathematics, 60(1):67–112, 2007. MR2270163 [Sim79] B. Simon. Functional integration and quantum physics, volume 86. Academic Press, 1979. MR0544188 [Sko56] A. Skorokhod. Limit theorems for stochastic processes. Theory of Probability & Its Applications, 1(3):261–290, 1956. MR0084897 [Sko57] A. Skorokhod. Limit theorems for stochastic processes with independent increments. Theory of Probability & Its Applications, 2(2):138–171, 1957. MR0094842 [SS10] O. Schramm and S. Sheffield. A contour line of the continuum Gaussian free field. Probability Theory and Related Fields, 1–34, 2010. MR3101840 [Ste70] E. M. Stein. Singular integrals and differentiability properties of functions, volume 2. Princeton University Press, 1970. MR0290095 [SW71] E. M. Stein and G. L. Weiss. Introduction to Fourier analysis on Euclidean spaces (PMS-32), volume 1. Princeton University Press, 1971. MR0304972 [SW13] X. Sun and W. Wu. Uniform spanning forests and the bi-Laplacian Gaussian field. arXiv preprint arXiv:1312.0059v1, 2013. [Tao10] T. Tao. An epsilon of room, I: Real analysis, volume 117 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2010. Pages from year three of a mathematical blog. MR2760403 [Tri83] H. Triebel. Theory of function spaces, volume 78 of Monographs in Mathematics. Birkhäuser Verlag, Basel, 1983. MR0781540 [Won70] E. Wong. Stochastic processes in information and dynamical systems. New York: McGraw-Hill, 1970. [Xia13] Y. Xiao. Recent developments on fractal properties of Gaussian random fields. In Further Developments in Fractals and Related Fields, pages 255–288. Springer, 2013. MR3184196 [Yag57] A. M. Yaglom. Some classes of random fields in n-dimensional space, related to stationary random processes. Theory of Probability & Its Applications, 2(3):273–320, 1957. MR0094844 |
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