## Michael Cranston

Professor, Mathematics
School of Physical Sciences

B.S., University of Minnesota, 1974
Ph.D., University of Minnesota, 1980, Mathematics

Phone: (949) 824-5507
Fax: (949) 824-7993
Email: mcransto@uci.edu

University of California, Irvine
540B Rowland Hall
Mail Code: 3875
Irvine, CA 92697
Publications
[53] A Central Limit Theorem for Isotropic Flows, with Yves LeJan, to appear Stochastic Processes and their Appl.

[52] A completely solvable continuum hompolymer model, with L. Koralov, S. Molchanov and B. Vainberg, submitted.

[51] A continuous model for homopolymers, with L. Koralov, S. Molchanov and B. Vainberg, Journal of Functional Analysis, Vol. 256, No. 8, 2656-2696, 2009.

[50] Homo- and hetero-polymers in the mean-field approximation. With O. Hryniv and S. Molchanov, Markov Processes and Related Fields, Vol. 15, No. 2, 205-224, 2009.

[49] On large deviations for the parabolic Anderson model, with D. Gauthier and T. Mountford, to appear PTRF.

[48] On large deviation regimes for random media models, with D. Gauthier and T. S. Mountford, Annals of Applied Probability, Vol. 19, No. 2, 826-862, 2009.

[47] A concentration inequality for isotropic random vectors, with S. Molchanov, submitted ECP.

[46] Quenched to annealed transition for the parabolic Anderson model, with S. Molchanov, Prob. Theory and Related Fields, 138 no, 1-2 , 177-193, 2007.

[45] Lyapunov exponent for the parabolic Anderson model in R^d, with T. Mountford. Journal of Functional Analysis. Vol. 236, 1, 78-119, July, 2006.

[44] Limit laws for sums of products of exponentials of iid random variables, with S. Molchanov, Israel Journal of Math, vol. 148, 115-136, 2005.

[43] Parabolic Anderson model with Levy noise, with T. Mountford and T. Shiga, Prob. Theory and Related Fields, 132, 321-355 , 2005.

[42] A spectral theory approach to homopolymer phase transitions, with S. Molchanov, Prob. And Math. Physics, CRM Proc. Lecture Notes 42, Amer. Math. Soc. Providence, RI, 2007.

[41]‘Lyapunov exponents for the parabolic Anderson model,’ with T.S. Mountford and T.Shiga, , Acta Mathematica Universitatis Comenianae, Vol. LXXI, 2(2002), pp. 163–188.

[40]‘Maximal height scaling of kinetically growing surfaces,’ with Y. Shapir, vol. 87, issue 13 Phy. Rev. Letters., 2001.

[39] ‘Dispersion rates under finite mode Kolmogorov flows’ with Scheutzow, Michael, Annals of Applied Prob., Vol. 12, No.2, 511-532, 2002.

[38] ‘On geometric properties of stochastic flows related to the Lyapunov spectrum,’ Prob Theory and Related Fields, 118, 1-16, 2000.

[37] ‘A condition for the equivalence of coupling and shift coupling’ with Wang, Feng-yu, Vol. 28,No.4, 1666-1679,Ann. of Probab., 2000.

[36] ‘Linear bounds for stochastic dispersion’ with Scheutzow, Michael; Steinsaltz, David, Vol. 28, No.4, 1852-1869, Ann. of Probab. ,2000.

[35] ‘Efficient coupling on the circle’ with Mountford, T.S., Game theory, optimal stopping, probability and statistics, 191--203, IMS Lecture Notes Monogr. Ser., 35, Inst. Math. Statist., Beachwood, OH, 2000.

[34] ‘Linear expansion of isotropic Brownian flows.’ With Scheutzow, Michael; Steinsaltz, David Electron. Comm. Probab. 4, 91—101, 1999.

[33] ‘Asymptotic curvature for stochastic dynamical systems.’ with Le Jan, Yves, Stochastic dynamics (Bremen, 1997), 327--338, Springer, New York, 1999.

[32] ‘Geometric evolution under isotropic stochastic flow.’ with LeJan, Y., ‘Electron. J. Probab. 3 no. 4, 36 pp. 1998.

[31] ‘Eigenfunction and harmonic function estimates in domains with horns and cusps.’ with Li, Yi, Comm. Partial Differential Equations 22, no. 11-12, 1805—1836, 1997.

[30] ‘Gromov's hyperbolicity and Picard's little theorem for harmonic maps.’ with Kendall, W. S., Kifer, Yu., Stochastic analysis and applications (Powys, 1995), 139--164, World Sci. Publishing, River Edge, NJ, 1996.

[29] ‘The strong law of large numbers for a Brownian polymer.’ with Mountford, T. S., Ann. Probab. 24, no. 3, 1300—1323, 1996.

[28] ‘Coupling and harmonic functions in the case of continuous time Markov processes.’ with Greven, Andreas, Stochastic Process. Appl. 60, no. 2, 261—286, 1995.

[27] ‘Self-attracting diffusions: two case studies.’ with Le Jan, Y., Math. Ann. 303, no. 1, 87—93, 1995.

[26] ‘Coupling constructions for hypoelliptic diffusions: two examples.’ with BenArous, Gerard; Kendall, Wilfrid S., Stochastic analysis (Ithaca, NY, 1993), 193--212, Proc. Sympos. Pure Math., 57, Amer. Math. Soc., Providence, RI, 1995.

[25] ‘A probabilistic approach to Martin boundaries for manifolds with ends.’ Probab. Theory Related Fields 96, no. 3, 319—334, 1993.

[24] ‘Martin boundaries of sectorial domains.’ with Salisbury, Thomas S. ,Ark. Mat. 31, no. 1, 27—49, 1993.

[23] ‘The radial part of Brownian motion. II. Its life and times on the cut locus.’ with Kendall, Wilfrid S.; March, Peter, Probab. Theory Related Fields 96, no. 3, 353—368, 1993.

[22] ‘A probabilistic approach to gradient estimates.’ Canad. Math. Bull. 35, no. 1, 46—55, 1992.

[21] ‘On specifying invariant $\sigma$-fields.’ Seminar on Stochastic Processes, 1991 (Los Angeles, CA, 1991), 15--37, Progr. Probab., 29, Birkhäuser Boston, Boston, MA, 1992.

[20] ‘Gradient estimates on manifolds using coupling.’ J. Funct. Anal. 99, no. 1, 110—124, 1991.

[19] ‘An extension of a result of Burdzy and Lawler.’ with Mountford, T. S., Probab. Theory Related Fields 89, no. 4, 487—502, 1991.

[18] ‘Noncoalescence for the Skorohod equation in a convex domain of ${R}\sp 2$.’ with Le Jan, Y., Probab. Theory Related Fields 87, no. 2, 241—252, 1990.

[17] ‘Some regularity results and eigenfunction estimates for the Schrödinger operator.’ with Zhao, Z., Diffusion processes and related problems in analysis, Vol. I (Evanston, IL, 1989), 139--147, Progr. Probab., 22, Birkhäuser Boston, Boston, MA, 1990.

[16] ‘Simultaneous boundary hitting for a two point reflecting Brownian motion.’ with Le Jan, Y., Séminaire de Probabilités, XXIII, 234--238, Lecture Notes in Math., 1372, Springer, Berlin, 1989.

[15] ‘On the noncoalescence of a two point Brownian motion reflecting on a circle.’ with Le Jan, Y., Ann. Inst. H. Poincaré Probab. Statist. 25, no. 2, 99—107, 1989.

[14] ‘Smoothness of the convex hull of planar Brownian motion.’ with Hsu, P.; March, P., Ann. Probab. 17, no. 1, 144—150, 1989.

[13] ‘Conditional Brownian motion, Whitney squares and the conditional gauge theorem.’ Seminar on Stochastic Processes, 1988 (Gainesville, FL, 1988), 109--119, Progr. Probab., 17, Birkhäuser Boston, Boston, MA, 1989.

[12] ‘Conditional gauge and potential theory for the Schrödinger operator.’ with Fabes, E.; Zhao, Z., Trans. Amer. Math. Soc. 307, no. 1, 171—194, 1988.

[11] ‘Conditional transformation of drift formula and potential theory for ${1\over 2}\Delta +b(·)·\nabla$.’ with Zhao, Z., Comm. Math. Phys. 112, no. 4, 613—625, 1987.

[10] ‘On the means of approach to the boundary of Brownian motion.’ Ann. Probab. 15, no.3, 1009—1013, 1987.

[9] ‘The Malliavin calculus for pure jump processes and applications to local time.’ with Bass, R. F Ann. Probab. 14, no. 2, 490—532, 1986.

[8] ‘Potential theory for the Schrödinger equation.’ with Fabes, E.; Zhao, Z., Bull. Amer. Math. Soc. (N.S.) 15, no. 2, 213—216, 1986.

[7] ‘Lifetime of conditioned Brownian motion in Lipschitz domains.’ Z. Wahrsch. Verw. Gebiete 70, no. 3, 335—340, 1985.

[6] ‘The lifetime of conditioned Brownian motion.’ with McConnell, T. R., Z. Wahrsch. Verw. Gebiete 65, no. 1, 1—11, 1983.

[5] ‘Invariant $\sigma$-fields for a class of diffusions.’ Z. Wahrsch. Verw. Gebiete 65, no. 2, 161—180, 1983.

[4] ‘Exit times for symmetric stable processes in ${R}\sp{n}$.’ with Bass, R. F., Ann. Probab. 11, no. 3, 578—588, 1983.

[3] ‘The Martin boundary of two-dimensional Ornstein- Uhlenbeck processes.’ with Orey, S.; Rösler, U., Probability, statistics and analysis, 63--78, London Math. Soc. Lecture Note Ser., 79, Cambridge Univ. Press, Cambridge-New York, 1983.

[2] ‘Brownian motion with lower class moving boundaries which grow faster than $t\sp{1/2}$.’ with Bass, R. F., Ann. Probab. 11, no. 1, 34—39, 1983.

[1] ‘Exterior Dirichlet problems and the asymptotic behavior of diffusions.’ with Orey, Steven; Rösler, Uwe, Stochastic differential systems (Proc. IFIP-WG 7/1 Working Conf., Vilnius, 1978), pp. 207--220, Lecture Notes in Control and Information Sci., 25, Springer, Berlin-New York, 1980.
Grants
NSF (PI) 2006-2009, $260,000 NSF FRG (CoPI) 2009-2112,$145,000
NSF (PI) 2004-2006, $100,000 GAANN (PI) 2006-2009,$660,000.
GAANN (PI) 2009-2112, \$524,00.
(Awarded NSF/NSA Grants from 1985-1989,1990-present.)
Other Experience
Professor
University of Rochester 1992—2004

Associate Professor
University of Rochester 1986—1991

Assistant Professor
University of Rochester 1982—1985

Visiting Professor
University of California, Los Angeles 1988—1989

Visiting Professor
University of Minnesota 1985—1986

Vistiing Professor
University of Washington 1983—1984

Visiting Lecturer
University of Illinois 1980—1982

Last updated
02/05/2010