Now showing items 1-20 of 112

    • 2-D Brownian motion in a system of reflecting barriers: effective diffusivity by a sampling method 

      Burdzy, Krzysztof; Holyst, Robert; Ingerman, David (Institute of Physics, 1994-02-07)
      We study two-dimensional Brownian motion in an ordered periodic system of linear reflecting barriers using the sampling method and conformal transformations. We calculate the effective diffusivity for the Brownian particle. ...
    • 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 ...
    • 3-connected configurations (n3) with no Hamiltonian circuit 

      Grünbaum, Branko (2006)
      For more than a century there have been examples of (n3) configurations without a Hamiltonian circuit. However, all these examples were only 2-connected. It has been believed that all geometric 3-connected configurations ...
    • {4,5} cubic lattice sponges 

      Gillispie, Steven; Grünbaum, Branko (2009-01-06)
    • Affine Partitions and Affine Grassmannians 

      Billey, Sara C.; Mitchell, Stephen C. (2008)
      We give a bijection between certain colored partitions and the elements in the quotient of an affine Weyl group modulo its Weyl group. By Bott’s formula these colored partitions give rise to some partition identities. In ...
    • An annihilating-branching particle model for the heat equation with average temperature zero 

      Burdzy, Krzysztof; Quastel, Jeremy (2005)
      We consider two species of particles performing random walks in a domain in [Real numbers] [superscript] d with reflecting boundary conditions, which annihilate on contact. In addition there is a conservation law so that ...
    • An asymptotically 4-stable process 

      Burdzy, Krzysztof; Madrecki, Andrzej (CRC Press, 1995)
      An asymptotically 4-stable process is constructed. The model identifies the 4-stable process with a sequence of processes converging in a very weak sense. It is proved that the 4-th variation of the process is a linear ...
    • The Bilinski dodecahedron, and assorted parallelohedra, zonohedra, monohedra, isozonohedra and otherhedra. 

      Grünbaum, Branko (2010)
      Fifty years ago Stanko Bilinski showed that Fedorov's enumeration of convex polyhedra having congruent rhombi as faces is incomplete, although it had been accepted as valid for the previous 75 years. The dodecahedron he ...
    • Bosonic Quantum Field Theory 

      Warner, Garth (2008-03-31)
      The purpose of these notes is to provide a systematic account of that part of Quantum Field Theory in which symplectic methods play a major role.
    • The boundary Harnack principle for non-divergence form elliptic operators 

      Burdzy, Krzysztof; Bass, Richard F. (Cambridge University Press, 1994)
      If L is a uniformly elliptic operator in non–divergence form, the boundary Harnack principle for the ratio of positive L–harmonic functions holds in Hölder domains of order [alpha] if [alpha] > 1/2. A counterexample shows ...
    • 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 ...
    • Brownian motion in a Brownian crack 

      Burdzy, Krzysztof; Khoshnevisan, Davar (Institute of Mathematical Statistics, 1998-08)
      Let D be the Wiener sausage of width [epsilon] around two-sided Brownian motion. The components of two-dimensional reflected Brownian motion in D converge to one-dimensional Brownian motion and iterated Brownian motion, ...
    • Brownian motion reflected on Brownian motion 

      Burdzy, Krzysztof; Nualart, David (Springer-Verlag GmbH, 2002-04)
      We study Brownian motion reflected on an "independent" Brownian path. We prove results on the joint distribution of both processes and the support of the parabolic measure in the space-time domain bounded by a Brownian ...
    • C*-Algebras 

      Warner, Garth (2010-11-15)
      This book is addressed to those readers who are already familiar with the elements of the theory but wish to go further. While some aspects, e.g. tensor products, are summarized without proof, others are dealt with in all ...
    • Can Every Face of a Polyhedron Have Many Sides? 

      Grünbaum, Branko (2008-11)
      The simple question of the title has many different answers, depending on the kinds of faces we are willing to consider, on the types of polyhedra we admit, and on the symmetries we require. Known results and open problems ...
    • A catalogue of simplicial arrangements in the real projective plane 

      Grünbaum, Branko (2005)
      An arrangement is the complex generated in the real projective plane by a family of straight lines that do not form a pencil. The faces of an arrangement are the connected components of the complement of the set of ...
    • Categorical Homotopy Theory 

      Warner, Garth (2012-01)
      This book is an account of certain developments in categorical homotopy theory that have taken place since the year 2000. Some aspects have been given the complete treatment (i.e., proofs in all detail), while others are ...
    • Censored stable processes 

      Burdzy, Krzysztof; Bogdan, Krzysztof; Chen, Zhen-Qing (Springer-Verlag GmbH, 2003-09)
      We present several constructions of a "censored stable process" in an open set D [is an element of the subset] R [to the power of] n, i.e., a symmetric stable process which is not allowed to jump outside D. We address ...
    • Coalescence of skew Brownian motions 

      Burdzy, Krzysztof; Barlow, Martin T.; Kaspi, Haya; Mandelbaum, Avi (Springer-Verlag, 2001)
      The purpose of this short note is to prove almost sure coalescence of two skew Brownian motions starting from different initial points, assuming that they are driven by the same Brownian motion. The result is very simple ...
    • Coalescence of synchronous couplings 

      Burdzy, Krzysztof; Chen, Zhen-Qing (Springer-Verlag GmbH, 2002-08)
      We consider a pair of reflected Brownian motions in a Lipschitz planar domain starting from different points but driven by the same Brownian motion. First we construct such a pair of processes in a certain weak sense, since ...