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  • Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions 

    Hu, Yaozhong; Liu, Yanghui; Nualart, David (American Meteorological Society, 2016-03-22)
    For a stochastic differential equation(SDE) driven by a fractional Brownian motion(fBm) with Hurst parameter H>12, it is known that the existing (naive) Euler scheme has the rate of convergence n1−2H. Since the limit H→12 ...
  • Fluctuations of TASEP and LPP with general initial data 

    Corwin, Ivan; Liu, Zhipeng; Wang, Dong (Institute of Mathematical Statistics, 2015-08-13)
    We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general lattice path to ...
  • A monotone Sinai theorem 

    Quas, Anthony; Soo, Terry (Institute of Mathematical Statistics, 2016-02-02)
    Sinai proved that a nonatomic ergodic measure-preserving system has any Bernoulli shift of no greater entropy as a factor. Given a Bernoulli shift, we show that any other Bernoulli shift that is of strictly less entropy ...
  • Quantitative stable limit theorems on the Wiener space 

    Nourdin, Ivan; Nualart, David; Peccati, Giovanni (Institute of Mathematical Statistics, 2016)
    We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings ...
  • On the intermittency front of stochastic heat equation driven by colored noises 

    Hu, Yaozhong; Huang, Jingyu; Nualart, David (Institute of Mathematical Statistics, 2016-03-01)
    We study the propagation of high peaks (intermittency fronts) of the solution to a stochastic heat equation driven by multiplicative centered Gaussian noise in RdRd. The noise is assumed to have a general homogeneous ...
  • Stability of Explicit One-Step Methods for P1-Finite Element Approximation of Linear Diffusion Equations on Anisotropic Meshes 

    Huang, Weizhang; Kamenski, Lennard; Lang, Jens (Society for Industrial and Applied Mathematics, 2016-05-26)
    We study the stability of explicit one-step integration schemes for the linear finite element approximation of linear parabolic equations. The derived bound on the largest permissible time step is tight for any mesh and ...
  • The Partitionability Conjecture 

    Duval, Art; Klivans, Caroline; Martin, Jeremy L. (American Mathematical Society, 2017-02)
    In 1979 Richard Stanley made the following conjecture: Every Cohen-Macaulay simplicial complex is partitionable. Motivated by questions in the theory of face numbers of simplicial complexes, the Partitionability Conjecture ...
  • Composing Scalable Nonlinear Algebraic Solvers 

    Brune, Peter R.; Knepley, Matthew G.; Smith, Barry F.; Tu, Xuemin (Society for Industrial and Applied Mathematics (SIAM), 2015-11-05)
    Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for ...
  • A FETI-DP TYPE DOMAIN DECOMPOSITION ALGORITHM FOR THREE-DIMENSIONAL INCOMPRESSIBLE STOKES EQUATIONS 

    Tu, Xuemin; Li, Jing (Society for Industrial and Applied Mathematics, 2015-03-03)
    The FETI-DP (dual-primal finite element tearing and interconnecting) algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp. 1235–1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp. 128–149] ...
  • Nonexistence of soliton-like solutions for defocusing generalized KdV equations 

    Kwon, Soonsik; Shao, Shuanglin (Texas State University, Department of Mathematics, 2015-02-24)
    We consider the global dynamics of the defocusing generalized KdV equation $$ \partial_t u + \partial_x^3 u = \partial_x(|u|^{p-1}u). $$ We use Tao's theorem [5] that the energy moves faster than the mass to prove a ...
  • On L2 modulus of continuity of Brownian local times and Riesz potentials 

    Deya, Aurelien; Nualart, David; Tindel, Samy (Institute of Mathematical Statistics, 2015-05-05)
    This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on three closely related problems: (a) Limit theorem for a Brownian modulus of continuity involving Riesz potentials, ...
  • Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency 

    Hu, Yaozhong; Huang, Jingyu; Nualart, David; Tindel, Samy (Institute of Mathematical Statistics, 2016-06-04)
    This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W is a mean zero Gaussian noise and the differential element uW is interpreted both in the sense of Skorohod and Stratonovich. ...
  • Density convergence in the Breuer-Major theorem for Gaussian stationary sequences 

    Hu, Yaozhong; Nualart, David; Tindel, Samy; Xu, Fangjun (Bernoulli Society for Mathematical Statistics and Probability, 2015)
    Consider a Gaussian stationary sequence with unit variance X={Xk;k∈N∪{0}}. Assume that the central limit theorem holds for a weighted sum of the form Vn=n−1/2∑n−1k=0f(Xk), where f designates a finite sum of Hermite ...
  • Effects of (Small) Permanent Charge and Channel Geometry on Ionic Flows via Classical Poisson--Nernst--Planck Models 

    Ji, Shuguan; Liu, Weishi; Zhang, Mingji (Society for Industrial and Applied Mathematics, 2015-01-15)
    In this work, we examine effects of permanent charges on ionic flows through ion channels via a quasi-one-dimensional classical Poisson--Nernst--Planck (PNP) model. The geometry of the three-dimensional channel is presented ...
  • Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations 

    Hur, Vera Mikyoung; Johnson, Mathew A. (Society for Industrial and Applied Mathematics, 2015-09-17)
    We study the stability and instability of periodic traveling waves for Korteweg--de Vries-type equations with fractional dispersion and related, nonlinear dispersive equations. We show that a local constrained minimizer ...
  • Simplicial and Cellular Trees 

    Duval, Art M.; Klivans, Caroline J.; Martin, Jeremy L. (Springer International Publishing, 2016-04-16)
    Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher ...
  • A Non-Partitionable Cohen-Macaulay Simplicial Complex 

    Duval, Art M.; Bennet, Goeckner; Klivans, Caroline J.; Martin, Jeremy L. (Elsevier, 2016-08-20)
    A long-standing conjecture of Stanley states that every Cohen–Macaulay simplicial complex is partitionable. We disprove the conjecture by constructing an explicit counterexample. Due to a result of Herzog, Jahan and Yassemi, ...
  • Cuts and flows of cell complexes 

    Duval, Art M.; Klivans, Caroline J.; Martin, Jeremy L. (Springer Verlag, 2014-10-15)
    We study the vector spaces and integer lattices of cuts and flows associated with an arbitrary finite CW complex, and their relationships to group invariants including the critical group of a complex. Our results extend ...
  • Enumerating Colorings, Tensions and Flows in Cell Complexes 

    Beck, Matthias; Breuer, Felix; Godkin, Logan; Martin, Jeremy L. (Elsevier, 2014-02)
    We study quasipolynomials enumerating proper colorings, nowhere-zero tensions, and nowhere-zero flows in an arbitrary CW-complex X, generalizing the chromatic, tension and flow polynomials of a graph. Our colorings, tensions ...
  • Pseudodeterminants and Perfect Square Spanning Tree Counts 

    Martin, Jeremy L.; Maxwell, Molly; Reiner, Victor; Wilson, Scott O. (International Press, 2015-06)
    The pseudodeterminant pdet(M) of a square matrix is the last nonzero coe cient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If @ is a symmetric or skewsymmetric matrix then ...

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