ResearchWorks Archive

Browsing Mathematics, Department of by Title

Browsing Mathematics, Department of by Title

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  • 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 ...
  • Burdzy, Krzysztof; Bass, Richard F. (American Mathematical Society, 1999-01)
    Let Z [subscript] t be two-dimensional Brownian motion. We say that a straight line L is a cut line if there exists a time t [is an element of the set] (0, 1) such that the trace of {Z [subscript] s : 0 [is less than or ...
  • 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 ...
  • 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 ...
  • 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 ...
  • Grünbaum, Branko (2008-06-05)
  • 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 ...
  • 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 ...
  • 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.
  • 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 ...
  • 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 ...
  • 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.
  • 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. ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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.
  • 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.
  • 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 ...

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