Precise asymptotics of small eigenvalues of reversible diffusions in the metastable regime [PDF]
, 2005 We investigate the close connection between metastability of the reversible diffusion process X defined by the stochastic differential equation dX_t=-\nabla F(X_t) dt+\sqrt2\epsilon dW_t,\qquad \epsilon >0, and the spectrum near zero of its generator -L_{
Eckhoff, Michael
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How often should you clean your room? [PDF]
, 2014 We introduce and study a combinatorial optimization problem motivated by the question in the title. In the simple case where you use all objects in your room equally often, we investigate asymptotics of the optimal time to clean up in terms of the number
Martin, Kimball, Shankar, Krishnan
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Precise asymptotics of the Ricci flow neckpinch [PDF]
Communications in Analysis and Geometry, 2007 The best known finite-time local Ricci flow singularity is the neckpinch, in which a proper subset of the manifold becomes geometrically close to a portion of a shrinking cylinder. In this paper, we prove precise asymptotics for rotationally symmetric Ricci flow neckpinches.
Angenent, Sigurd, Knopf, Dan
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Precise Asymptotics on Second-Order Complete Moment Convergence of Uniform Empirical Process
Abstract and Applied Analysis, 2014 Let {ξi,1≤i≤n} be a sequence of iid U[0, 1]-distributed random variables, and define the uniform empirical process Fn(t)=n-1/2∑i=1n(I{ξi≤t}-t),0≤t≤1, Fn=sup0≤t≤1|Fn(t)|.
Junshan Xie, Lin He
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Precise spectral asymptotics for nonautonomous logistic equations of population dynamics in a ball
Abstract and Applied Analysis, 2005 We consider the semilinear elliptic eigenvalue problem −Δu+k(|x|)up=λu, u>0 in BR, u=0 on ∂BR, where p>1 is a constant, BR:={x∈RN:|x|0 is a parameter. We investigate the global structure of the branch of (λ,uλ) of bifurcation diagram from a point of view
Tetsutaro Shibata
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Quantifying tolerance of a nonlocal multi-qudit state to any local noise
, 2018 We present a general approach for quantifying tolerance of a nonlocal N-partite state to any local noise under different classes of quantum correlation scenarios with arbitrary numbers of settings and outcomes at each site.
Loubenets, Elena R.
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Precise tail asymptotics of fixed points of the smoothing transform with general weights [PDF]
, 2014 We consider solutions of the stochastic equation $R=_d\sum_{i=1}^NA_iR_i+B$, where $N>1$ is a fixed constant, $A_i$ are independent, identically distributed random variables and $R_i$ are independent copies of $R$, which are independent both from $A_i$'s
Buraczewski, D. +2 more
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Precise Asymptotic Approximations for Kernels Corresponding to Lévy Processes [PDF]
Potential Analysis, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jo, Sihun, Yang, Minsuk
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Precise asymptotics for the parabolic Anderson model with a moving catalyst or trap [PDF]
, 2010 We consider the solution $u\colon [0,\infty) \times\mathbb{Z}^d\rightarrow [0,\infty) $ to the parabolic Anderson model, where the potential is given by $(t,x)\mapsto\gamma\delta_{Y_t}(x)$ with $Y$ a simple symmetric random walk on $\mathbb{Z}^d ...
Schnitzler, Adrian, Wolff, Tilman
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Precise asymptotics of certain Wiener functionals
Journal of Functional Analysis, 1991 An asymptotic expansion is given for a class of Wiener functionals as the variance \(s\) of the underlying Wiener measure tends to zero. The asymptotic expansion is obtained via a stochastic analogue of Taylors formula. In order to prove this formula, the authors develop a time- dependent version of the Malliavin calculus based upon the heat (as ...
Kusuoka, Shigeo, Stroock, Daniel W
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