ResearchWorks Archive

Browsing Mathematics, Department of by Title

Browsing Mathematics, Department of by Title

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  • 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 ...
  • 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.
  • Banuelos, Rodrigo; Bass, Richard F.; Burdzy, Krzysztof (Duke University Press, 1991-10)
    A version of the boundary Harnack principle is proven.
  • Burdzy, Krzysztof; Bass, Richard F.; Khoshnevisan, Davar (Institute of Mathematical Statistics, 1994-04)
    For each a [is an element of the set] (0, 1/2), there exists a random measure [beta] [subscript] a which is supported on the set of points where two-dimensional Brownian motion spends a units of local time. The measure ...
  • Grünbaum, Branko (Springer New York, 1997)
    A prismatoid is a polyhedron with all vertices in two parallel planes. A polyhedron P is isogonal if all its vertices form one transitivity class under isometric symmetries of P. Although these restrictions appear very ...
  • Burdzy, Krzysztof; San Martin, Jaime (Institute of Mathematical Statistics, 1995-10)
    Suppose [epsilon] [is a member of the set] [0, 1) and let theta [subscipt epsilon] (t) = (1 − [epsilon]) [square root of] (2tln [subscript] 2 t). Let L [to the power of epsilon] [subscript] t denote the amount of local ...
  • Burdzy, Krzysztof; Madrecki, Andrzej (Institute of Mathematical Statistics, 1996-02)
    An Ito-type formula is given for an asymptotically 4-stable process.
  • Burdzy, Krzysztof (Institute of Mathematics, 1995)
    Suppose that X is a two-dimensional Brownian motion. The trace X[0, 1] contains a self-avoiding continuous path whose Hausdorff dimension is equal to 2.
  • Warner, Garth (2009-01-12)
    My original set of lectures on Mechanics was divided into three parts: Lagrangian Mechanics, Hamiltonian Mechanics, Equivariant Mechanics. The present text is an order of magnitude expansion of the first part and is ...
  • Grünbaum, Branko (1997)

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