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作者：Klenke, Achim; Mytnik, Leonid
作者单位：Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
摘要：Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence (2008) Preprint] and [Ann. Probab. 38 (2010) 479-497]. For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.
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作者：Grigor'yan, Alexander; Telcs, Andras
作者单位：University of Bielefeld; Budapest University of Technology & Economics
摘要：We prove equivalent conditions for two-sided sub-Gaussian estimates of heat kernels on metric measure spaces.
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作者：Sheffield, Scott; Sun, Nike
作者单位：Massachusetts Institute of Technology (MIT); Stanford University
摘要：We show that, under mild assumptions on the limiting curve, a sequence of simple chordal planar curves converges uniformly whenever certain Loewner driving functions converge. We extend this result to random curves. The random version applies in particular to random lattice paths that have chordal SLE kappa as a scaling limit, with kappa < 8 (nonspace-filling). Existing SLE kappa convergence proofs often begin by showing that the Loewner driving functions of these paths (viewed from infinity) ...
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作者：Dumitriu, Ioana; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of vertices, the empirical spectral distribution converges to the semicircle law. Moreover, we prove concentration estimates on the number of eigenvalues over progressively smaller intervals. We also show that, with high probability, all the eigenvectors are delocalized.
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作者：Diehl, Joscha; Friz, Peter
作者单位：Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Backward stochastic differential equations (BSDEs) in the sense of Pardoux-Peng [Lecture Notes in Control and Inform. Sci. 176 (1992) 200-217] provide a non-Markovian extension to certain classes of nonlinear partial differentia] equations; the nonlinearity is expressed in the so-called driver of the BSDE. Our aim is to deal with drivers which have very little regularity in time. To this end, we establish continuity of BSDE solutions with respect to rough path metrics in the sense of Lyons [Re...
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作者：Miller, Jason; Peres, Yuval
作者单位：Stanford University; Microsoft
摘要：We show that the measure on markings of Z(n)(d), d >= 3, with elements of {0, 1} given by i.i.d. fair coin flips on the range R of a random walk X run until time T and 0 otherwise becomes indistinguishable from the uniform measure on such markings at the threshold T = 1/2 T-cov (Z(n)(d)). a consequence of our methods, we show that the total variation mixing time of the random walk on the lamplighter graph Z(2) (sic) Z(n)(d), d >= 3, has a cutoff with threshold 1/2 T-cov (Z(n)(d)). We give a ge...
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作者：Chen, Xia
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：Let B-s be a d-dimensional Brownian motion and omega(dx) be an independent Poisson field on R-d. The almost sure asymptotics for the logarithmic moment generating function logE(0) exp{+/-theta integral(t)(0)(V) over bar (B-s)ds} (t -> infinity) are investigated in connection with the renormalized Poisson potential of the form (V) over bar (x) = integral(Rd) 1/vertical bar y - x vertical bar(p)[omega(dy) - dy], x is an element of R-d. The investigation is motivated by some practical problems ar...
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作者：Hammond, Alan
作者单位：University of Oxford
摘要：We study the droplet that results from conditioning the planar subcritical Fortuin-Kasteleyn random cluster model on the presence of an open circuit Gamma(0) encircling the origin and enclosing an area of at least (or exactly) n(2). We consider local deviation of the droplet boundary, measured in a radial sense by the maximum local roughness, MLR(Gamma(0)), this being the maximum distance from a point in the circuit Gamma(0) to the boundary a conv(Gamma(0)) of the circuit's convex hull; and in...
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作者：Hu, Yaozhong; Lu, Fei; Nualarti, David
作者单位：University of Kansas
摘要：In this paper, a Feynman-Kac formula is established for stochastic partial differential equation driven by Gaussian noise which is, with respect to time, a fractional Brownian motion with Hurst parameter H < 1/2. To establish such a formula, we introduce and study a nonlinear stochastic integral from the given Gaussian noise. To show the Feynman-Kac integral exists, one still needs to show the exponential integrability of nonlinear stochastic integral. Then, the approach of approximation with ...
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作者：Kolb, Martin; Steinsaltz, David
作者单位：University of Oxford
摘要：This paper extends and clarifies results of Steinsaltz and Evans [Trans. Amer. Math. Soc. 359 (2007) 1285-1234], which found conditions for convergence of a killed one-dimensional diffusion conditioned on survival, to a quasistationary distribution whose density is given by the principal eigenfunction of the generator. Under the assumption that the limit of the killing at infinity differs from the principal eigenvalue we prove that convergence to quasistationarity occurs if and only if the pri...
