Browsing Mathematics, Department of by Title
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Comparison of potential theoretic properties of rough domains
(2005)We discuss the relationships between the notion of intrinsic ultracontractivity, parabolic Harnack principle, compactness of the 1resolvent of the Neumann Laplacian, and nontrap property for Euclidean domains with finite ... 
Conditioned Brownian motion in planar domains
(SpringerVerlag GmbH, 199504)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 FlemingViottype model and probabilistic interpretation of Laplacian eigenfunctions
(Institute of Physics, 19960607)We analyze and simulate a twodimensional Brownian multitype particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in the twodimensional box, ... 
Configurations of points and lines
(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
(Princeton University and Institute for Advanced Study, 199901)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
(SpringerVerlag GmbH, 199601)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
(NorthHolland (Elsevier), 198910)Let f be a (random) realvalued 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 nonnegative and f(0) = ... 
Cut points on Brownian paths
(Institute of Mathematical Statistics, 198907)Let X be a standard twodimensional 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
(American Mathematical Society, 199901)Let Z [subscript] t be twodimensional 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
(American Physical Society, 199907)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 ... 
Efficient Markovian couplings: Examples and counterexamples
(Institute of Mathematical Statistics, 200005)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 ... 
Eigenvalue expansions for Brownian motion with an application to occupation times
(Institute of Mathematical Statistics, 19960131)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 ... 
An enduring error
(20080605) 
Erratum to The Supremum of Brownian Times on Hölder Curves
(Birkhauser, 20020521)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 ... 
Euler's ratiosum theorem and generalizations
(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, higherdimensional ... 
Excursion laws and exceptional points on Brownian paths
(SpringerVerlag, 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. 
Fast equilibrium selection by rational players living in a changing world
(The Econometric Society, 200101)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 riskdominant equilibrium. More precisely, a ... 
Fiber Brownian motion and the "hot spots" problem
(Duke University Press, 200010)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 ... 
Fibrations and Sheaves
(20121213)The purpose of this book is to give a systematic treatment of fibration theory and sheaf theory, the emphasis being on the foundational essentials. 
A FlemingViat particle representation of Dirichlet Laplacian
(SpringerVerlag GmbH, 200011)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. ...