Publication list for Bruce K. Driver
(also see Math Reviews)




B. K. Driver: “Convergence of the U(1)4 Lattice Gauge Theory to Its Continuum Limit,” (extract from thesis), Comm. Math.  Physics, 110 (1987), 479-501.


B. K. Driver: “Classification of Bundle Connection Pairs by Parallel Translations and Lassos,” J. Func. Analysis, 83, No. 1l (1989), 185-231.


B. K. Driver: “YM2: Continuum Expectations, Lattice Convergence, and Lassos,” Comm. Math. Physics., 123, (1989), 575-616.


B. K. Driver and R. D. Driver: “Simplicity of Solutions of x'(t)= bx(t-1),” J. of Math. Anal. & Appl., 157, no. 2 (1991), 591-608.


B. K. Driver: “Two dimensional Euclidean quantized Yang-Mills fields,” (G. J. Morrow and W-S. Yang, eds.), Proc Conf. on Probability Models in Mathematical Physics, Colorado Springs, 1990, World Scientific, N.J. (1991), 21-36.


B. K. Driver and M. Röckner: “Construction of diffusions on path and loop spaces of compact Riemannian manifolds,” C.R. Acad. of Sci. Paris, December 315, Série I (1992), 603-608.


B. K. Driver: “A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold,” J. Funct. Anal. 110 (1992), 272-376.


B. K. Driver and T. Frankel: “On the growth of waves on manifolds,” Journal of Mathematical Analysis & Applications, 178 (1993), 143-155.


B. K. Driver: “A Cameron-Martin type quasi-invariance theorem for pinned Brownian motion on a compact Riemannian manifold,” Trans. of Amer. Math. Soc., 342 (1994), 375-395.


B. K. Driver: “The non-equivalence of Dirichlet forms on path spaces,” in Stochastic analysis on infinite dimensional spaces, (H. Kunita, and H.-H. Kuo eds), Pitman Notes in Mathematics Series 310, Longman Scientific & Technical, Essex England (1994), 75-88.


B. K. Driver: “Loop space, curvature, and quasi-invariance,” lecture notes from Centro Vito Volterra for Lectures given Fall of 1992.


B. K. Driver: “Towards calculus and geometry on path spaces,” in “Stochastic Analysis, Summer Institute on Stochastic Analysis,” July 11-30, 1993, Cornell University (Eds. M. Cranston and M. Pinsky), Proceedings of Symposia in Pure Mathematics, Vol. 57, American Mathematical Society, Rhode Island, 1995, pp. 405-422.


B. K. Driver: “On the Kakutani-Ito-Segal-Gross and the Segal-Bargmann-Hall isomorphisms,” J. of Funct. Anal. 133 (1995), 69-128.


B. K. Driver and Yaozhong Hu:  “On the heat kernel logarithmic Sobolev inequalities, Proceedings of the Fifth Greygynog Symposium, Stochastic Analysis and Applications,” (I.M. Davies, A. Truman, and K.D. Elworthy Eds.), World Scientific, New Jersey 1996, p. 189-200.


B. K. Driver: “A primer on Riemannian geometry and stochastic analysis on path spaces,” F.I.M. series of the ETH (Zurich, Switzerland).


B. K. Driver and L. Gross:  “Hilbert spaces of holomorphic functions on complex Lie groups,” New trends in stochastic analysis (Charigworth, 1994) (1997), pp. 76-106. 


B. K. Driver and T. Lohrenz:  “Logarithmic Sobolev inequalities for pinned loop groups,” J. of Funct. Anal. 140(2) (1996), pp. 381-448. 


B. K. Driver: “Integration by parts for heat kernel measures revisited,” J. Math. Pures Appl. (9) 76(8) (1997), pp. 703-737. 


B. K. Driver: “Integration by parts and quasi-invariance for heat kernel measures on loop groups,” J. Funct. Anal. 149(2) (1997), pp. 470-547. 


B. K. Driver: Correction to (A19a) published in J. Funct. Anal. 155(1) (1998), pp. 297-301. 


B. K. Driver: “Stochastic analysis,” Bulletin of the Amer. Math.Society 35 (1998), pp. 99-104.  


B. K. Driver and B. C. Hall: “Yang-Mills theory and the Segal-Bargmann transforms,” Comm. Math. Phys. 201(2) (1999), pp. 249-290. 


B. K. Driver: “The Lie bracket of adapted vector fields on Wiener spaces,” Appl. Math. Optim 39(2) (1999), pp. 179-210.


L. Andersson and B. K. Driver: “Finite dimensional approximations to Wiener measure and path integral formulas on manifolds,” J. of Functional Analysis 165 (1999), pp. 430-498. 


B. K. Driver and B.C. Hall: The energy representation has no non-zero fixed vectors.  In Stochastic processes, physics and geometry: new interplays, II (Leipzig, 1999), pages 143-155. Amer. Math. Soc., Providence, RI, 2000. 


Shigeki Aida and Bruce K. Driver: Equivalence of heat kernel measure and pinned Wiener measure on loop groups.  C. R. Acad. Sci. Paris Sér. I Math., 331(9):709-712, 2000. 


Bruce K. Driver and Anton Thalmaier: Heat equation derivative formulas for vector bundles.  J. Funct. Anal., 183(1):42-108, 2001.


Bruce K. Driver and Vikram K. Srimurthy: Absolute continuity of heat  kernel measure with pinned Wiener measure on loop groups.  Ann. Probab., 29(2):691-723, 2001. 

(A28) Bruce K. Driver: Heat kernels measures and infinite dimensional analysis.  Heat kernels and analysis on manifolds, graphs, and metric spaces (Paris, 2002), 101--141, Contemp. Math., 338, Amer. Math. Soc., Providence, RI, 2003.
(A29) Driver, Bruce K.:  Analysis of Wiener measure on path and loop groups. Finite and infinite dimensional analysis in honor of Leonard Gross (New Orleans, LA, 2001), 57--85, Contemp. Math., 317, Amer. Math. Soc., Providence, RI, 2003.
(A30) Driver, Bruce K.: Curved Wiener space analysis. Real and stochastic analysis, 43--198, Trends Math., Birkhäuser Boston, Boston, MA, 2004.
(A31) Driver, Bruce K.; Melcher, Tai: Hypoelliptic heat kernel inequalities on the Heisenberg group. J. Funct. Anal. 221 (2005), no. 2, 340--365.
(A32) Arnaudon, Marc; Driver, Bruce K.: and Anton Thalmaier.  Gradient Estimates for Positive Harmonic Functions by Stochastic Analysis. Accepted  by Stochastic Processes and their Applications, page 19 pages., 2006.


Driver, Bruce K.; Gross, Leonard; and Saloff-Coste, Laurent: Holomorphic functions and subelliptic heat kernels over Lie groups. Journal of the European Mathematical Society,  Volume 11 Issue 5 (2009),  941--978.


Cecil, Matthew; and Driver, Bruce K.: Heat kernel measure on loop and path groups. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11 (2008), no. 2, 135--156.


Driver, Bruce K.; and  Gordina, Maria: Heat kernel analysis on infinite-dimensional Heisenberg groups. J. Funct. Anal. 255 (2008), no. 9, 2395--2461.


Driver, Bruce K.; Gross, Leonard; and Saloff-Coste, Laurent: Surjectivity of the Taylor map for complex nilpotent Lie groups. Mathematical Proceedings of the Cambridge Philosophical Society 146 (2009), no. 1, 177--195.


Driver, Bruce K.; and Gordina, Maria: Square integrable holomorphic functions on infinite-dimensional Heisenberg type groups. Journal Probability Theory and Related Fields, Published online: 1 April 2009.   0178-8051 (Print) 1432-2064 (Online), p. 1-48.


Driver, Bruce K.; and  Gordina, Maria: Integrated Harnack inequalities on Lie groups, Journal of Differential Geometry,  83  (2009) no. 3, 501--550.


Driver, Bruce K.; Gross, Leonard; and Saloff-Coste, Laurent: Growth of Taylor coefficients over complex homogeneous spaces. To appear in the Tohoku Mathematical Journal, 62 (September, 2010). no. 3, 51 pages.


B. Other Work:


(B1) B. K. Driver: “Convergence of the U(1)4 Lattice Gauge Theory to Its Continuum Limit,” Cornell University  (1986). THESIS

C. Work in Progress:

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08/15/2016 02:53 PM