ResearchWorks Archive

Browsing EPrint Collection - Mathematics by Title

Browsing EPrint Collection - Mathematics by Title

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  • 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 ...
  • 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.
  • 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, ...
  • 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, ...
  • 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 ...
  • 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 ...
  • 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) = ...
  • 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 ...
  • 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 ...
  • 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 ...
  • Burdzy, Krzysztof; Kendall, Wilfrid S. (Institute of Mathematical Statistics, 2000-05)
    In this paper we study the notion of an efficient coupling of Markov processes. Informally, an efficient coupling is one which couples at the maximum possible exponential rate, as given by the spectral gap. This notion ...
  • Burdzy, Krzysztof; Bass, Richard F. (Institute of Mathematical Statistics, 1996-01-31)
    Let B be a Borel subset of R [to the power of] d with finite volume. We give an eigenvalue expansion for the transition densities of Brownian motion killed on exiting B. Let A [subscript] 1 be the time spent by Brownian ...
  • Grünbaum, Branko (2008-06-05)
  • Bass, Richard F.; Burdzy, Krzysztof (Birkhauser, 2002-05-21)
    For [function] f [maps the set]: [0, 1] [into the set] [Real numbers], we consider L [superscript] f [subscript] t , the local time of spacetime Brownian motion on the curve f. Let S [subscript][sigma] be the class of all ...
  • Grünbaum, Branko; Klamkin, Murray S. (2005)
    A theorem of Euler concerns sums of ratios in which Cevians of a triangle are divided by a common point. Generalizations of this result in three directions are presented: polygons instead of triangles, higher-dimensional ...
  • Burdzy, Krzysztof (Springer-Verlag, 1993)
    The purpose of this note is to present an example of a family of "exceptional points" on Brownian paths which cannot be constructed using an entrance law.
  • 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. ...

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