Preprints - IAM Publications


	2015 Louis-Pierre Arguin, Anton Bovier and Nicola Kistler An ergodic theorem for the extremal process of branching Brownian motion Ann. Inst. Henri Poincaré Probab. Stat., 51(2): 557--569 2015 http://dx.doi.org/10.1214/14-AIHP608

	Mathias Beiglböck, Martin Huesmann and Florian Stebegg Root to Kellerer ArXiv e-print 2015 http://arxiv.org/abs/1507.07690

	Mathias Beiglböck, Alexander M. G. Cox, Martin Huesmann, Nicolas Perkowski and David J. Prömel Pathwise super-replication via Vovk's outer measure ArXiv e-prints 2015 http://arxiv.org/abs/1504.03644

	Peter Bella, Michael Goldman and Barbara Zwicknagl Study of Island Formation in Epitaxially Strained Films on Unbounded Domains Arch. for Ration. Mech. and Anal., 218(1): 163-217 2015 http://dx.doi.org/10.1007/s00205-015-0858-x

	Benjamin Berkels, Alexander Effland and Martin Rumpf A Posteriori Error Control for the Binary Mumford-Shah Model ArXiv Preprint 2015 http://arxiv.org/abs/1505.05284 Abstract: The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to object reconstruction. This paper presents robust a posteriori error estimates for a natural error quantity, namely the area of the non properly segmented region. To this end, a suitable strictly convex and non-constrained relaxation of the originally non-convex functional is investigated and Repin's functional approach for a posteriori error estimation is used to control the numerical error for the relaxed problem in the $L^2$-norm. In combination with a suitable cut out argument, a fully practical estimate for the area mismatch is derived. This estimate is incorporated in an adaptive meshing strategy. Two different adaptive primal-dual finite element schemes, and the most frequently used finite difference discretization are investigated and compared. Numerical experiments show qualitative and quantitative properties of the estimates and demonstrate their usefulness in practical applications.

	Benjamin Berkels, Alexander Effland and Martin Rumpf Time Discrete Geodesic Paths in the Space of Images SIAM J. Imaging Sci., 8(3): 1457-1488 2015 http://dx.doi.org/10.1137/140970719 Abstract: In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and effective variational time discretization of geodesics paths is proposed. This requires to minimize a discrete path energy consisting of a sum of consecutive image matching functionals over a set of image intensity maps and pairwise matching deformations. For square-integrable input images the existence of discrete, connecting geodesic paths defined as minimizers of this variational problem is shown. Furthermore, Γ-convergence of the underlying discrete path energy to the continuous path energy is proved. This includes a diffeomorphism property for the induced transport and the existence of a square-integrable weak material derivative in space and time. A spatial discretization via finite elements combined with an alternating descent scheme in the set of image intensity maps and the set of matching deformations is presented to approximate discrete geodesic paths numerically. Computational results underline the efficiency of the proposed approach and demonstrate important qualitative properties.

	S. Beuchler, K. Hofer, D. Wachsmuth and J.-E. Wurst Boundary concentrated finite elements for optimal control problems with distributed observation Comput. Optim. Appl., 62(1): 31--65 2015 http://dx.doi.org/10.1007/s10589-015-9737-5

	Alexei Borodin and Patrik L. Ferrari Random tilings and Markov chains for interlacing particles ArXiv e-prints 2015 http://arxiv.org/abs/1506.03910

	Anton Bovier and Martina Baar From stochastic, individual-based models to the canonical equation of adaptive dynamics -- in one step 2015 http://arxiv.org/abs/1505.02421

	Anton Bovier and Lisa B. Hartung Variable speed branching Brownian motion 1. Extremal processes in the weak correlation regime Lat. Am. J. Probab. Math. Stat., 12(1): 261-291 2015 http://alea.impa.br/articles/v12/12-11.pdf Abstract: We prove the convergence of the extremal processes for variable speed branching Brownian motions where the ”speed functions”, that describe the timeinhomogeneous variance, lie strictly below their concave hull and satisfy a certain weak regularity condition. These limiting objects are universal in the sense that they only depend on the slope of the speed function at 0 and the final time t. The proof is based on previous results for two-speed BBM obtained in Bovier and Hartung (2014) and uses Gaussian comparison arguments to extend these to the general case.

	Anton Bovier and Hannah Mayer A conditional strong large deviation result and a functional central limit theorem for the rate function ALEA Lat. Am. J. Probab. Math. Stat., 12(1): 533--550 2015 http://alea.impa.br/articles/v12/12-21.pdf

	Tristan Buckmaster and Herbert Koch The Korteweg--de Vries equation at H- 1 regularity Ann. I. H. Poincaré - AN, 32: 1071-1098 2015 http://dx.doi.org/10.1016/j.anihpc.2014.05.004 Abstract: In this paper we will prove the existence of weak solutions to the Korteweg-de Vries initial value problem on the real line with H^-1 initial data; moreover, we will study the problem of orbital and asymptotic H^s stability of solitons for integers s≥ -1; finally, we will also prove new a priori H^-1 bounds for solutions to the Korteweg-de Vries equation. The paper will utilise the Miura transformation to link the Korteweg-de Vries equation to the modified Korteweg-de Vries equation.

	Annegret Y. Burtscher and Roland Donninger Hyperboloidal evolution and global dynamics for the focusing cubic wave equation 2015 http://arxiv.org/abs/1511.08600

	Brandon Runnels, Irene Beyerlein, Sergio Conti and Michael Ortiz A relaxation method for the energy and morphology of grain boundaries and interfaces J. Mech. Phys. Solids 2015 http://dx.doi.org/10.1016/j.jmps.2015.11.007

	Juan J. L. Velázquez and Jogia Bandyopadhyay Blow-up rate estimates for the solutions of the bosonic Boltzmann-Nordheim equation J. Math. Phys., 56(Art. 063302): 1-29 2015 http://arxiv.org/abs/1411.5460 Abstract: In this paper, we study the behavior of a class of mild solutions of the homogeneous and isotropic bosonic Boltzmann-Nordheim equation near the blow-up. We obtain some estimates on the blow-up rate of the solutions and prove that, as long as a solution is bounded above by the critical singularity 1x1x (the equilibrium solutions behave like this power law near the origin), it remains bounded in the uniform norm. In Sec. III of the paper, we prove a local existence result for a class of measure-valued mild solutions, which is of independent interest and which allows us to solve the Boltzmann-Nordheim equation for some classes of unbounded densities.

	2014 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.

	Mario Bebendorf Low-rank approximation of elliptic boundary value problems with high-contrast coefficients 2014 http://arxiv.org/abs/1410.3717

	Mathias Beiglböck, Alexander M.G. Cox and Martin Huesmann Optimal Transport and Skorokhod Embedding ArXiv eprints 2014 http://arxiv.org/abs/1307.3656 Abstract: The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of the important classical problems in probability theory and a number of authors have constructed solutions with particular optimality properties. These constructions employ a variety of techniques ranging from excursion theory to potential and PDE theory and have been used in many different branches of pure and applied probability. We develop a new approach to Skorokhod embedding based on ideas and concepts from optimal mass transport. In analogy to the celebrated article of Gangbo and McCann on the geometry of optimal transport, we establish a geometric characterization of Skorokhod embeddings with desired optimality properties. This leads to a systematic method to construct optimal embeddings. It allows us, for the first time, to derive all known optimal Skorokhod embeddings as special cases of one unified construction and leads to a variety of new embeddings. While previous constructions typically used particular properties of Brownian motion, our approach applies to all sufficiently regular Markov processes.

	Alexei Borodin, Ivan Corwin, Patrik L. Ferrari and Balint Vető Height fluctuations for the stationary KPZ equation Math. Phys. Anal. Geom., 18(1, Art. 20): 1-95 2014 http://arxiv.org/abs/1407.6977 Abstract: We compute the one-point probability distribution for the stationary KPZ equation (i.e. initial data $\mathcal{H}(0,X)=B(X)$, for $B(X)$ a two-sided standard Brownian motion) and show that as time $T$ goes to infinity, the fluctuations of the height function $\mathcal{H}(T,X)$ grow like $T^{1/3}$ and converge to those previously encountered in the study of the stationary totally asymmetric simple exclusion process, polynuclear growth model and last passage percolation. The starting point for this work is our derivation of a Fredholm determinant formula for Macdonald processes which degenerates to a corresponding formula for Whittaker processes. We relate this to a polymer model which mixes the semi-discrete and log-gamma random polymers. A special case of this model has a limit to the KPZ equation with initial data given by a two-sided Brownian motion with drift $β$ to the left of the origin and $b$ to the right of the origin. The Fredholm determinant has a limit for $β>b$, and the case where $β=b$ (corresponding to the stationary initial data) follows from an analytic continuation argument.

	Anton Bovier and Lisa B. Hartung The extremal process of two-speed branching Brownian motion Electron. J. Probab., 19(Art. 18): 1-28 2014 http://dx.doi.org/10.1214/EJP.v19-2982 Abstract: We construct and describe the extremal process for variable speed branching Brownian motion, studied recently by Fang and Zeitouni \citeFZ_BM, for the case of piecewise constant speeds; in fact for simplicity we concentrate on the case when the speed is $\sigma_1$ for $s\leq bt$ and $\sigma_2$ when $bt\leq s\leq t$. In the case $\sigma_1>\sigma_2$, the process is the concatenation of two BBM extremal processes, as expected. In the case $\sigma_1<\sigma_2$, a new family of cluster point processes arises, that are similar, but distinctively different from the BBM process. Our proofs follow the strategy of Arguin, Bovier, and Kistler.

2015

2014