Now showing items 1-20 of 112

    • Unsolved Problems in Intuitive Geometry 

      Klee, Victor (1960)
    • Lectures on Arrangements 

      Grünbaum, Branko (1974)
    • On Brownian Excursions in Lipschitz Domains. Part II: Local Asymptotic Distributions 

      Burdzy, Krzysztof; Toby, Ellen H.; Williams, Ruth J. (Birkhäuser Boston, Inc., 1989)
      In this paper, we continue the study initiated in Burdzy and Williams (1986) of the local properties of Brownian excursions in Lipschitz domains. The focus in part I was on local path properties of such excursions. In ...
    • Geometric Properties of 2-dimensional Brownian Paths 

      Burdzy, Krzysztof (Springer-Verlag GmbH, 1989)
      Let A be the set of all points of the plane C, visited by two-dimensional Brownian motion before time 1. With probability 1, all points of A are "twist points" except a set of harmonic measure zero. "Twist points" may be ...
    • Cut points on Brownian paths 

      Burdzy, Krzysztof (Institute of Mathematical Statistics, 1989-07)
      Let X be a standard two-dimensional Brownian motion. There exists a.s. t [is an element of the set] (0; 1) such that X([0; t))[intersected with] X((t; 1]) = [empty set]. It follows that X([0; 1]) is not homeomorphic to ...
    • Curvature of the convex hull of planar Brownian motion near its minimum point 

      Burdzy, Krzysztof; San Martin, Jaime (North-Holland (Elsevier), 1989-10)
      Let f be a (random) real-valued function whose graph represents the boundary of the convex hull of planar Brownian motion run until time 1 near its lowest point in a coordinate system so that f is non-negative and f(0) = ...
    • A representation of local time for Lipschitz surfaces 

      Banuelos, Rodrigo; Bass, Richard F.; Burdzy, Krzysztof (Springer-Verlag GmbH, 1990)
      Suppose that D [is an element of the set of Real numbers to the power of n], n [is greater than or equal to] 2, is a Lipschitz domain and let N[subscript]t(r) be the number of excursions of Brownian motion inside D with ...
    • Non-intersection exponents for Brownian paths. Part I: Existence and an invariance principle 

      Burdzy, Krzysztof; Lawler, Gregory F. (Springer-Verlag GmbH, 1990)
      Let X and Y be independent three-dimensional Brownian motions, X(0) = (0; 0; 0), Y (0) = (1; 0; 0) and let p [subscript]r = P(X[0; r] [intersected with] Y [0; r] = [empty set]. Then the "non- intersection exponent" [from] ...
    • A probabilistic proof of the boundary Harnack principle 

      Burdzy, Krzysztof; Bass, Richard F. (Birkhauser Boston, Inc., 1990)
      The main purpose of this paper is to give a probabilistic proof of Theorem 1.1, one using elementary properties of Brownian motion. We also obtain the fact that the Martin boundary equals the Euclidean boundary as an easy ...
    • Percolation dimension of fractals 

      Burdzy, Krzysztof (Academic Press (Elsevier), 1990-01)
      "Percolation dimension" is introduced in this note. It characterizes certain fractals and its definition is based on the Hausdorff dimension. It is shown that percolation dimension and "boundary dimension" are in a sense ...
    • Non-intersection exponents for Brownian paths. Part II: Estimations and applications to a random fractal. 

      Burdzy, Krzysztof; Lawler, Gregory F. (Institute of Mathematical Statistics, 1990-07)
      Let X and Y be independent two-dimensional Brownian motions, X(0) = (0; 0); Y(0) = ([epsilon]; 0), and let p([epsilon]) = P(X[0; 1] [intersected with] Y [0; 1] = [empty set], q([epsilon]) = {Y [0; 1] does not contain a ...
    • On non-increase of Brownian motion 

      Burdzy, Krzysztof (Institute of Mathematical Statistics, 1990-07)
      A new proof of the non-increase of Brownian paths is given.
    • Minimal Fine Derivatives and Brownian Excursions 

      Burdzy, Krzysztof (Nagoya University, 1990-09)
      Let f be an analytic function defined on D [is a subset of] [complex numbers] C. If [the derivative of the function f at the point x] has a limit when [the set] x [into the set] z [is an element of the set partial derivative] ...
    • A boundary Harnack principle in twisted Hölder domains 

      Burdzy, Krzysztof; Bass, Richard F. (Annals of Mathematics, 1991-09)
      The boundary Harnack principle for the ratio of positive harmonic functions is shown to hold in twisted Hölder domains of order [alpha] for [alpha is an element of the set](1/2, 1]. For each [alpha is an element of the ...
    • Hölder domains and the boundary Harnack principle 

      Banuelos, Rodrigo; Bass, Richard F.; Burdzy, Krzysztof (Duke University Press, 1991-10)
      A version of the boundary Harnack principle is proven.
    • 2-D Brownian motion in a system of traps: Application of conformal transformations 

      Burdzy, Krzysztof; Holyst, Robert; Salisbury, Thomas S. (Institute of Physics, 1992)
      We study two-dimensional Brownian motion in a periodic system of traps using conformal transformations. The system is periodic in the x and y directions. We calculate the ratio of the drift along the y-axis to the drift ...
    • Hitting a boundary point with reflected Brownian motion 

      Burdzy, Krzysztof; Marshall, Donald E. (Springer-Verlag, 1992)
      An explicit integral test involving the reflection angle is given for the reflected Brownian motion in a half-plane to hit a fixed boundary point.
    • Lifetimes of conditioned diffusions 

      Burdzy, Krzysztof; Bass, Richard F. (Springer-Verlag GmbH, 1992)
      We investigate when an upper bound on expected lifetimes of conditioned diffusions associated with elliptic operators in divergence and non-divergence form can be found. The critical value of the parameter is found for ...
    • The Martin boundary in non-Lipschitz domains 

      Burdzy, Krzysztof; Bass, Richard F. (American Mathematical Society, 1993)
      The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean boundary in C [to the power of gamma] domains, where [gamma](x) = ...
    • A three-dimensional Brownian path reflected on a Brownian path is a free Brownian path 

      Burdzy, Krzysztof (Springer Science+Business Media B.V., 1993)
      Three-dimensional Brownian path reflected on Brownian path is a free Brownian path.