Now showing items 73-92 of 112

    • Omittable lines 

      Grünbaum, Branko (2005)
      Every finite family of (straight) lines in the projective plane, not forming a pencil, is well know to have at least one "ordinary point" –– that is, a point common to precisely two of the lines. A line of a family is ...
    • On Brownian Excursions in Lipschitz Domains. Part II: Local Asymptotic Distributions 

      Burdzy, Krzysztof; Toby, Ellen H.; Williams, Ruth J. (Birkhäuser Boston, Inc., 1989)
      In this paper, we continue the study initiated in Burdzy and Williams (1986) of the local properties of Brownian excursions in Lipschitz domains. The focus in part I was on local path properties of such excursions. In ...
    • On domain monotonicity of the Neumann heat kernel 

      Burdzy, Krzysztof; Bass, Richard F. (Academic Press (Elsevier), 1993-08-15)
      Some examples are given of convex domains for which domain monotonicity of the Neumann heat kernel does not hold.
    • On minimal parabolic functions and time-homogenous parabolic h-transforms 

      Burdzy, Krzysztof; Salisbury, Thomas S. (American Mathematical Society, 1999-03-29)
      Does a minimal harmonic function h remain minimal when it is viewed as a parabolic function? The question is answered for a class of long thin semi-infinite tubes D [is an element of the subset of real numbers to the power ...
    • On Neumann eigenfunctions in lip domains 

      Burdzy, Krzysztof; Atar, Rami (American Mathematical Society, 2004)
      A "lip domain" is a planar set lying between graphs of two Lipschitz functions with constant 1. We show that the second Neumann eigenvalue is simple in every lip domain except the square. The corresponding eigenfunction ...
    • On nodal lines of Neumann eigenfunctions 

      Burdzy, Krzysztof; Atar, Rami (Institute of Mathematical Statistics, 2002-06-03)
      We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain.
    • On non-increase of Brownian motion 

      Burdzy, Krzysztof (Institute of Mathematical Statistics, 1990-07)
      A new proof of the non-increase of Brownian paths is given.
    • On the "hot spots" conjecture of J. Rauch 

      Burdzy, Krzysztof; Banuelos, Rodrigo (Academic Press (Elsevier), 1999-05-10)
      We will state several rigorous versions of J. Rauch's "hot spots" conjecture, review some known results, and prove the conjecture under some additional assumptions. Let us, however, first observe that the conclusion ...
    • On the Robin problem in fractal domains 

      Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing (2005)
      We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum is greater than 0, and some other families of domains where it is ...
    • On the time and direction of stochastic bifurcation 

      Burdzy, Krzysztof; Frankel, David M.; Pauzner, Ady (Elsevier, 1998)
      This paper is a mathematical companion to an article introducing a new economics model, by Burdzy, Frankel and Pauzner (1997). The motivation of this paper is applied, but the results may have some mathematical interest ...
    • Percolation dimension of fractals 

      Burdzy, Krzysztof (Academic Press (Elsevier), 1990-01)
      "Percolation dimension" is introduced in this note. It characterizes certain fractals and its definition is based on the Hausdorff dimension. It is shown that percolation dimension and "boundary dimension" are in a sense ...
    • Positivity 

      Warner, Garth (2009-12-23)
      These notes provide a systematic account of certain aspects of the statistical structure of quantum theory. Here the all prevailing notion is that of a completely positive map and Stinespring's famous characterization ...
    • Positivity of Brownian transition densities 

      Burdzy, Krzysztof; Barlow, Martin T.; Bass, Richard F. (Electronic Journal of Probability, 1997-09-24)
      Let B be a Borel subset of R [to the power of] d and let p(t, x, y) be the transition densities of Brownian motion killed on leaving B. Fix x and y in B. If p(t, x, y) is positive for one t, it is positive for every value ...
    • A probabilistic proof of the boundary Harnack principle 

      Burdzy, Krzysztof; Bass, Richard F. (Birkhauser Boston, Inc., 1990)
      The main purpose of this paper is to give a probabilistic proof of Theorem 1.1, one using elementary properties of Brownian motion. We also obtain the fact that the Martin boundary equals the Euclidean boundary as an easy ...
    • Reconstruction Theory 

      Warner, Garth (2011-01)
      Suppose that G is a compact group. Denote by \underline{Rep} G the category whose objects are the continuous finite dimensional unitary representations of G and whose morphisms are the intertwining operators--then ...
    • Reduction of dimensionality in a diffusion search process and kinetics of gene expression 

      Burdzy, Krzysztof; Holyst, Robert; Blazejezyk, M.; Goralski, G.; Bocquet, L. (North-Holland (Elsevier), 2000-03-01)
      In order to activate a gene in a DNA molecule a specific protein (transcription factor) has to bind to the promoter of the gene. We formulate and partially answer the following question: how much time does a transcription ...
    • A representation of local time for Lipschitz surfaces 

      Banuelos, Rodrigo; Bass, Richard F.; Burdzy, Krzysztof (Springer-Verlag GmbH, 1990)
      Suppose that D [is an element of the set of Real numbers to the power of n], n [is greater than or equal to] 2, is a Lipschitz domain and let N[subscript]t(r) be the number of excursions of Brownian motion inside D with ...
    • Sets avoided by Brownian motion 

      Burdzy, Krzysztof; Adelman, Omer; Pemantle, Robin (Institute of Mathematical Statistics, 1998-04)
      A fixed two-dimensional projection of a three-dimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the two-dimensional projections with probability one? Equivalently: ...
    • Shocks and Business Cycles 

      Frankel, David M.; Burdzy, Krzysztof (2005)
      A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this model has a unique ...
    • Shocks and business cycles 

      Burdzy, Krzysztof; Frankel, David M. (Berkeley Electronic Press, 2005)
      A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this model has a unique ...