Now showing items 1-20 of 84

    • 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 ...
    • 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 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 ...
    • 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, ...
    • 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) = ...
    • Cut points on Brownian paths 

      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 ...
    • Cutting Brownian Paths 

      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 ...
    • Diffusion on curved, periodic surfaces 

      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 ...