Now showing items 30-49 of 112

    • Diffusion on curved, periodic surfaces 

      Burdzy, Krzysztof; Holyst, Robert; Plewezynski, D.; Aksimentiev, A. (American Physical Society, 1999-07)
      We present a simulation algorithm for a diffusion on a curved surface given by the equation [omega](r)50. The algorithm is tested against analytical results known for diffusion on a cylinder and a sphere, and applied to ...
    • Efficient Markovian couplings: Examples and counterexamples 

      Burdzy, Krzysztof; Kendall, Wilfrid S. (Institute of Mathematical Statistics, 2000-05)
      In this paper we study the notion of an efficient coupling of Markov processes. Informally, an efficient coupling is one which couples at the maximum possible exponential rate, as given by the spectral gap. This notion ...
    • Eigenvalue expansions for Brownian motion with an application to occupation times 

      Burdzy, Krzysztof; Bass, Richard F. (Institute of Mathematical Statistics, 1996-01-31)
      Let B be a Borel subset of R [to the power of] d with finite volume. We give an eigenvalue expansion for the transition densities of Brownian motion killed on exiting B. Let A [subscript] 1 be the time spent by Brownian ...
    • An enduring error 

      Grünbaum, Branko (2008-06-05)
    • Erratum to The Supremum of Brownian Times on Hölder Curves 

      Bass, Richard F.; Burdzy, Krzysztof (Birkhauser, 2002-05-21)
      For [function] f [maps the set]: [0, 1] [into the set] [Real numbers], we consider L [superscript] f [subscript] t , the local time of spacetime Brownian motion on the curve f. Let S [subscript][sigma] be the class of all ...
    • Euler's ratio-sum theorem and generalizations 

      Grünbaum, Branko; Klamkin, Murray S. (2005)
      A theorem of Euler concerns sums of ratios in which Cevians of a triangle are divided by a common point. Generalizations of this result in three directions are presented: polygons instead of triangles, higher-dimensional ...
    • Excursion laws and exceptional points on Brownian paths 

      Burdzy, Krzysztof (Springer-Verlag, 1993)
      The purpose of this note is to present an example of a family of "exceptional points" on Brownian paths which cannot be constructed using an entrance law.
    • Fast equilibrium selection by rational players living in a changing world 

      Burdzy, Krzysztof; Frankel, David M.; Pauzner, Ady (The Econometric Society, 2001-01)
      We study a coordination game with randomly changing payoffs and small frictions in changing actions. Using only backwards induction, we find that players must coordinate on the risk-dominant equilibrium. More precisely, a ...
    • Fiber Brownian motion and the "hot spots" problem 

      Burdzy, Krzysztof; Bass, Richard F. (Duke University Press, 2000-10)
      We show that in some planar domains both extrema of the second Neumann eigenfunction lie strictly inside the domain. The main technical innovation is the use of "fiber Brownian motion," a process which switches between ...
    • Fibrations and Sheaves 

      Warner, Garth (2012-12-13)
      The purpose of this book is to give a systematic treatment of fibration theory and sheaf theory, the emphasis being on the foundational essentials.
    • A Fleming-Viat particle representation of Dirichlet Laplacian 

      Burdzy, Krzysztof; Holyst, Robert; March, Peter (Springer-Verlag GmbH, 2000-11)
      We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. ...
    • A Gaussian oscillator 

      Burdzy, Krzysztof; White, David (Institute of Mathematical Statistics, 2004-10-06)
      We present a stochastic process with sawtooth paths whose distribution is given by a simple rule and whose stationary distribution is Gaussian. The process arose in a natural way in research on interaction of an inert ...
    • 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 ...
    • Graphs of polyhedra; polyhedra as graphs 

      Grünbaum, Branko (2005)
      Relations between graph theory and polyhedra are presented in two contexts. In the first, the symbiotic dependence between 3-connected planar graphs and convex polyhedra is described in detail. In the second, a theory of ...
    • The Heat Equation and Reflected Brownian Motion in Time-Dependent Domains 

      Burdzy, Krzysztof; Chen, Zhen-Qing; Sylvester, John (Institute of Mathematical Statistics, 2004-01)
      The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as "non-cylindrical domains," and its connections with partial differential equations. Construction ...
    • The heat equation in time dependent domains with insulated boundaries 

      Burdzy, Krzysztof; Chen, Zhen-Qing; Sylvester, John (Academic Press (Elsevier), 2004-10)
      The paper studies, among other things, two types of possible singularities of the solution to the heat equation at the boundary of a moving domain. Several explicit results on "heat atoms" and "heat singularities" are given.
    • 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.
    • Homotopical Topos Theory 

      Warner, Garth (2012-05)
      The purpose of this book is two-fold: (1) To give a systematic introduction to topos theory from a purely categorical point of view, thus ignoring all logical and algebraic issues. (2) To give an account of the homotopy ...
    • The "hot spots" problem in planar domains with one hole. 

      Burdzy, Krzysztof (Duke University Press, 2005)
      There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside the domain.
    • 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.