| 2016Herbert Koch, Angkana Rüland and Wenhui Shi
The variable coefficient thin obstacle problem: Carleman inequalities
Adv. Math., 301: 820--866 2016
http://dx.doi.org/10.1016/j.aim.2016.06.023
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| Jan Maas, Martin Rumpf and Stefan Simon
Generalized optimal transport with singular sources
2016
http://arxiv.org/abs/1607.01186
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| Celia Reina, Anja Schlömerkemper and Sergio Conti
Derivation of $\bf F=\bf F^\rm e\bf F^\rm p$ as the continuum limit of crystalline slip
J. Mech. Phys. Solids, 89: 231--254 2016
10.1016/j.jmps.2015.12.022
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| 2015Sebastian Andres, Jean-Dominique Deuschel and Martin Slowik
Invariance principle for the random conductance model in a degenerate ergodic environment
Ann. Probab., 43(4): 1866-1891 2015
http://dx.doi.org/10.1214/14-AOP921
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| Sebastian Andres, Jean-Dominique Deuschel and Martin Slowik
Harnack inequalities on weighted graphs and some applications to the random conductance model
Probab. Theory Relat. Fields: 1-47 2015
http://dx.doi.org/10.1007/s00440-015-0623-y
Abstract: We establish elliptic and parabolic Harnack inequalities on graphs with unbounded weights. As an application we prove a local limit theorem for a continuous time random walk X in an environment of ergodic random conductances taking values in (0,∞) satisfying some moment conditions. |
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| Mathias Beiglböck, Martin Huesmann and Florian Stebegg
Root to Kellerer
ArXiv e-print 2015
http://arxiv.org/abs/1507.07690
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| Roland Donninger and Birgit Schörkhuber
Stable blowup for wave equations in odd space dimensions
2015
http://arxiv.org/abs/1504.00808
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| Alexander Effland, Martin Rumpf, Stefan Simon, Kirsten Stahn and Benedikt Wirth
Bézier curves in the space of images
In Proceedings Scale Space and Variational Methods in Computer Vision, Volume 9087 of Lecture Notes in Computer Science
page 372-384.
Publisher: Springer International
2015
http://dx.doi.org/10.1007/978-3-319-18461-6_30
Abstract: Bézier curves are a widespread tool for the design of curves in Euclidian space. This paper generalizes the notion of Bézier curves to the infinite-dimensional space of images. To this end the space of images is equipped with a Riemannian metric which measures the cost of image transport and intensity variation in the sense of the metamorphosis model by Miller and Younes. Bézier curves are then computed via the Riemannian version of de Casteljau's algorithm, which is based on a hierarchical scheme of convex combination along geodesic curves. Geodesics are approximated using a variational discretization of the Riemannian path energy. This leads to a generalized de Casteljau method to compute suitable discrete Bézier curves in image space. Selected test cases demonstrate qualitative properties of the approach. Furthermore, a Bézier approach for the modulation of face interpolation and shape animation via image sketches is presented. |
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| Alberto Enciso, Daniel Peralta-Salas and Stefan Steinerberger
Prescribing the nodal set of the first eigenfunction in each conformal class
2015
http://arxiv.org/abs/1503.05105
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| Matthias Erbar, Kazumasa Kuwada and Karl-Theodor Sturm
On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
Invent. Math., 201(3): 993-1071 2015
http://dx.doi.org/10.1007/s00222-014-0563-7
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| Patrik L. Ferrari, Herbert Spohn and Thomas Weiss
Scaling Limit for Brownian Motions with One-sided Collisions
Ann. Appl. Probab., 25(3): 1349-1382 2015
http://dx.doi.org/10.1214/14-AAP1025
Abstract: We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Schütz-type formula is derived for the transition probability. We investigate an infinite system with periodic initial configuration, i.e., particles are located at the integer lattice at time zero. The joint distribution of the positions of a finite subset of particles is expressed as a Fredholm determinant with a kernel defining a signed determinantal point process. In the appropriate large time scaling limit, the fluctuations in the particle positions are described by the Airy\(_1\) process. |
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| Patrik L. Ferrari, Herbert Spohn and Thomas Weiss
Brownian motions with one-sided collisions: the stationary case
Electronic Journal of Probability, 20(Art. 69): 1-41 2015
http://dx.doi.org/10.1214/EJP.v20-4177
Abstract: We consider an infinite system of Brownian motions which interact through a given Brownian motion being reflected from its left neighbor. Earlier we studied this system for deterministic periodic initial configurations. In this contribution we consider initial configurations distributed according to a Poisson point process with constant intensity, which makes the process space-time stationary. We prove convergence to the Airy process for stationary the case. As a byproduct we obtain a novel representation of the finite-dimensional distributions of this process. Our method differs from the one used for the TASEP and the KPZ equation by removing the initial step only after the large time limit. This leads to a new universal cross-over process. |
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| Nicola Gigli, Tapio Rajala and Karl-Theodor Sturm
Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below
J. Geom. Anal. 2015
http://arxiv.org/abs/1305.4849
Abstract: We prove existence and uniqueness of optimal maps on RCD∗(K,N) spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation and to the local-to-global property of RCD∗(K,N) bounds. |
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| Herbert Koch, Angkana Rüland and Wenhui Shi
The Variable Coefficient Thin Obstacle Problem: Optimal Regularity and Regularity of the Regular Free Boundary
2015
http://arXiv.org/abs/1504.03525
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| Herbert Koch and Stefan Steinerberger
Convolution Estimates for Singular Measures and Some Global Nonlinear Brascamp-Lieb Inequalities
Proceedings of the Royal Society of Edinburgh, Section: A Mathematics, 145(6): 1223-1237 2015
http://arxiv.org/abs/1404.4536
Abstract: We give an L2 x L2 → L2 convolution estimate for singular measures supported on transversal hypersurfaces in ℝn, which improves earlier results of Bejenaru et al. as well as Bejenaru and Herr. The quantities arising are relevant to the study of the validity of bilinear estimates for dispersive partial differential equations. We also prove a class of global, nonlinear Brascamp–Lieb inequalities with explicit constants in the same spirit. |
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| Stefan Steinerberger
Dispersion dynamics for the defocusing generalized Korteweg-de Vries equation
Proc. Amer. Math. Soc., 143(2): 789-800 2015
http://dx.doi.org/10.1090/S0002-9939-2014-12285-4
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| Karl-Theodor Sturm
Metric Measure Spaces with Variable Ricci Bounds and Couplings of Brownian Motions
In Zhen-Qing Chen, Niels Jacob, Masayoshi Takeda, Toshihiro Uemura, editor, Festschrift Masatoshi Fukushima, Volume 17 of Interdisciplinary Mathematical Sciences
Chapter 27, page 553-575.
2015
http://dx.doi.org/10.1142/9789814596534_0027
Abstract: The goal of this paper is twofold: we study metric measure spaces (X, d, m) with variable lower bounds for the Ricci curvature and we study pathwise coupling of Brownian motions. Given any lower semicontinuous function k : X → ℝ we introduce the curvature-dimension condition CD(k, ∞) which canonically extends the curvature-dimension condition CD(K, ∞) of Lott-Sturm-Villani for constant K ∈ R. For infinitesimally Hilbertian spaces we prove
its equivalence to an evolution-variation inequality EVIk which in turn extends the EVIK-inequality of Ambrosio-Gigli-Savaré;
its stability under convergence and its local-to-global property.
For metric measure spaces with uniform lower curvature bounds K we prove that for each pair of initial distributions µ1, µ2 on X there exists a coupling , t ≥ 0, of two Brownian motions on X with the given initial distributions such that a.s. |
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| 2014Sebastian Andres, Jean-Dominique Deuschel and Martin Slowik
Heat kernel estimates for random walks with degenerate weights
2014
http://arxiv.org/abs/1412.4338
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| Gerard Barkema, Patrik L. Ferrari, Joel L. Lebowitz and Herbert Spohn
KPZ universality class and the anchored Toom interface
Phys. Rev. E, 90(Art. 042116) 2014
http://dx.doi.org/10.1103/PhysRevE.90.042116
Abstract: We revisit the anchored Toom interface and use KPZ scaling theory to argue that the interface fluctuations are governed by the Airy1 process with the role of space and time interchanged. There is no free parameter. The predictions are numerically well confirmed for space-time statistics in the stationary state. In particular the spatial fluctuations of the interface are given by the GOE edge distribution of Tracy and Widom. |
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| Patrick Diehl and Marc A. Schweitzer
Efficient Neighbor Search for Particle Methods on GPUs
In M. Griebel and M. A. Schweitzer, editor, Meshfree Methods for Partial Differential Equations VII, Volume 100 of Lecture Notes in Computational Science and Engineering
Chapter 5, page 81-95.
Publisher: Springer International
2014
http://dx.doi.org/10.1007/978-3-319-06898-5_5
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