Now showing items 8-27 of 112

    • 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 ...
    • Comparison of potential theoretic properties of rough domains 

      Burdzy, Krzysztof; Chen, Zhen-Qing (2005)
      We discuss the relationships between the notion of intrinsic ultracontractivity, parabolic Harnack principle, compactness of the 1-resolvent of the Neumann Laplacian, and non-trap property for Euclidean domains with finite ...
    • Conditioned Brownian motion in planar domains 

      Burdzy, Krzysztof; Bass, Richard F. (Springer-Verlag GmbH, 1995-04)
      We give an upper bound for the Green functions of conditioned Brownian motion in planar domains. A corollary is the conditional gauge theorem in bounded planar domains.
    • Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions 

      Burdzy, Krzysztof; Holyst, Robert; Ingerman, David; March, Peter (Institute of Physics, 1996-06-07)
      We analyze and simulate a two-dimensional Brownian multi-type particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in the two-dimensional box, ...
    • Configurations of points and lines 

      Grünbaum, Branko (2005)
      A vigorous study of geometric configurations started in the 1870's but was essentially abandoned early in the twentieth century. New approaches found during the last two decades prompted a renewed interest in the topic, ...
    • A counterexample to the "hot spots" conjecture 

      Burdzy, Krzysztof; Werner, Wendelin (Princeton University and Institute for Advanced Study, 1999-01)
      We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with Neumann boundary conditions ...
    • A critical case for Brownian slow points 

      Burdzy, Krzysztof; Bass, Richard F. (Springer-Verlag GmbH, 1996-01)
      Let X [subscript] t be a Brownian motion and let S(c) be the set of reals r [is greather than or equal to] 0 such that |X ([subscript] r+t) − X [subscript] r| [is less than or equal to] c [square root of] t, 0 [is less ...
    • 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) = ...