 2017Matthias Erbar, Martin Rumpf, Bernhard Schmitzer and Stefan Simon
Computation of Optimal Transport on Discrete Metric Measure Spaces
Unknown
https://arxiv.org/abs/1707.06859

 
 P.L. Ferrari and A. Occelli
Universality of the GOE TracyWidom distribution for TASEP with arbitrary particle density
preprint: arXiv:1704.01291 2017
https://arxiv.org/abs/1704.01291
Abstract: We consider TASEP in continuous time with nonrandom initial conditions and arbitrary fixed density of particles. We show GOE TracyWidom universality of the onepoint fluctuations of the associated height function. The result phrased in last passage percolation language is the universality for the pointtoline problem where the line has an arbitrary slope. 
 
 P.L. Ferrari, P. Ghosal and P. Nejjar
Limit law of a second class particle in TASEP with nonrandom initial condition
preprint: arXiv:1710.02323 2017
https://arxiv.org/abs/1710.02323
Abstract: We consider the totally asymmetric simple exclusion process (TASEP) with nonrandom initial condition having density $\rho$ on $\mathbb{Z}_$ and $\lambda$ on $\mathbb{Z}_+$, and a second class particle initially at the origin. For $\rho<\lambda$, there is a shock and the second class particle moves with speed $1\lambda\rho$. For large time $t$, we show that the position of the second class particle fluctuates on a $t^{1/3}$ scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time $t$. 
 
 P.L. Ferrari
Finite GUE distribution with cutoff at a shock
preprint: arXiv:1712.00102 2017
https://arxiv.org/abs/1712.00102
Abstract: We consider the totally asymmetric simple exclusion process with initial conditions generating a shock. The fluctuations of particle positions are asymptotically governed by the randomness around the two characteristic lines joining at the shock. We describe this in terms of spacetime correlations, without employing the mapping to the last passage percolation. We then consider a special case, where the asymptotic distribution is a cutoff of the distribution of the largest eigenvalue of a finite GUE matrix. Finally we discuss the strength of the probabilistic and physically motivated approach and compare it with the mathematical difficulties of a direct computation. 
 
 Behrend Heeren, Martin Rumpf and Benedikt Wirth
Variational time discretization of Riemannian splines
IMA J. Numer. Anal. 2017
https://arxiv.org/abs/1711.06069

 
 Nora Lüthen, Martin Rumpf, Sascha Tölkes and Orestis Vantzos
Branching Structures in Elastic Shape Optimization
2017
https://arxiv.org/abs/1711.03850
Abstract: Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer. The paper discusses the optimization of such supporting structures in a specific class of domain patterns in 2D, which composes of periodic and branching period transitions on subdomain facets. These investigations can be considered as a case study to display examples of optimal branching domain patterns. In explicit, a rectangular domain is decomposed into rectangular subdomains, which share facets with neighbouring subdomains or with facets which split on one side into equally sized facets of two different subdomains. On each subdomain one considers an elastic material phase with stiff elasticity coefficients and an approximate void phase with orders of magnitude softer material. For given load on the outer domain boundary, which is distributed on a prescribed fine scale pattern representing the contact area of the shape, the interior elastic phase is optimized with respect to the compliance cost. The elastic stress is supposed to be continuous on the domain and a stress based finite volume discretization is used for the optimization. If in one direction equally sized subdomains with equal adjacent subdomain topology line up, these subdomains are consider as equal copies including the enforced boundary conditions for the stress and form a locally periodic substructure. An alternating descent algorithm is employed for a discrete characteristic function describing the stiff elastic subset on the subdomains and the solution of the elastic state equation. Numerical experiments are shown for compression and shear load on the boundary of a quadratic domain. 
 
 Jan Maas, Martin Rumpf and Stefan Simon
Transport based image morphing with intensity modulation
In Proc. of International Conference on Scale Space and Variational Methods in Computer Vision
Publisher: Springer, Cham
2017
http://dx.doi.org/10.1007/9783319587714_45

 
 B. Niethammer Marco Bonacini and J.J. L. Velázquez
Selfsimilar solutions to coagulation equations with timedependent tails: the case of homogeneity smaller than one
2017
https://arxiv.org/abs/1704.08905

 
 Barbara Niethammer Marco Bonacini and J.J. L. Velázquez
Selfsimilar solutions to coagulation equations with timedependent tails: the case of homogeneity one
2017
https://arxiv.org/abs/1612.06610

 
 Alessia Nota, Sergio Simonella and Juan J.L. Velázquez
On the theory of the Lorentz gases with long range interactions
2017
https://arxiv.org/abs/1707.04193

 
 Celia Reina and Sergio Conti
Incompressible inelasticity as an essential ingredient for the validity of the kinematic decomposition $F=F^eF^i$
J. Mech. Phys. Solids, 107: 322342 2017
10.1016/j.jmps.2017.07.004

 
 Angkana Rüland, Christian Zillinger and Barbara Zwicknagl
Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int($K^lc$)
2017
https://arxiv.org/abs/1709.02880

 
 J.J. L. Velázquez and Raphael Winter
From a nonMarkovian system to the Landau equation
2017
https://arxiv.org/abs/1707.07544

 
 2016Stefan Adams, Roman Kotecký and Stefan Müller
Strict Convexity of the Surface Tension for Nonconvex Potentials
2016
http://arxiv.org/abs/1606.09541v1

 
 Sebastian Andres and Lisa B. Hartung
Diffusion processes on branching Brownian motion
2016
https://arxiv.org/abs/1607.08132

 
 S. Andres and L. Hartung
Diffusion processes on branching Brownian motion
ArXiv eprints 2016
http://adsabs.harvard.edu/abs/2016arXiv160708132A

 
 V. Beffara, S. Chhita and K. Johansson
Airy point process at the liquidgas boundary
arXiv:1606.08653 2016
http://arxiv.org/abs/1606.08653
Abstract: {Domino tilings of the twoperiodic Aztec diamond feature all of the three possible types of phases of random tiling models. These phases are determined by the decay of correlations between dominoes and are generally known as solid, liquid and gas. The liquidsolid boundary is easy to define microscopically and is known in many models to be described by the Airy process in the limit of a large random tiling. The liquidgas boundary has no obvious microscopic description. Using the height function we define a random measure in the twoperiodic Aztec diamond designed to detect the long range correlations visible at the liquidgas boundary. We prove that this random measure converges to the extended Airy point process. This indicates that, in a sense, the liquidgas boundary should also be described by the Airy process.} 
 
 A. Borodin, I. Corwin and P.L. Ferrari
Anisotropic (2+1)d growth and Gaussian limits of qWhittaker processes
arXiv:1612.00321 2016
https://arxiv.org/abs/1612.00321
Abstract: We consider a discrete model for anisotropic (2+1)dimensional growth of an interface height function. Owing to a connection with qWhittaker functions, this system enjoys many explicit integral formulas. By considering certain Gaussian stochastic differential equation limits of the model we are able to prove a spacetime limit to the (2+1)dimensional additive stochastic heat equation (or EdwardsWilkinson equation) along characteristic directions. In particular, the bulk height function converges to the Gaussian free field which evolves according to this stochastic PDE. 
 
 S. Chhita, P.L. Ferrari and H. Spohn
Limit distributions for KPZ growth models with spatially homogeneous random initial conditions
preprint, arXiv:1611.06690 2016
http://arxiv.org/abs/1611.06690
Abstract: For stationary KPZ growth in 1+1 dimensions the height fluctuations are governed by the BaikRains distribution. Using the totally asymmetric single step growth model, alias TASEP, we investigate height fluctuations for a general class of spatially homogeneous random initial conditions. We prove that for TASEP there is a oneparameter family of limit distributions, labeled by the roughness of the initial conditions. The distributions are defined through a variational formula. We use Monte Carlo simulations to obtain their numerical plots. Also discussed is the connection to the sixvertex model at is conical point. 
 
 Sergio Conti, Martin Rumpf, Rüdiger Schultz and Sascha Tölkes
Stochastic Dominance Constraints in Elastic Shape Optimization
2016
https://arxiv.org/abs/1606.09461
Abstract: This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from finitedimensional stochastic programming to shape optimization. Rather than handling risk aversion in the objective, this enables risk aversion by including dominance constraints that single out subsets of nonanticipative shapes which compare favorably to a chosen stochastic benchmark. This new class of stochastic shape optimization problems arises by optimizing over such feasible sets. The analytical description is built on riskaverse cost measures. The underlying cost functional is of compliance type plus a perimeter term, in the implementation shapes are represented by a phase field which permits an easy estimate of a regularized perimeter. The analytical description and the numerical implementation of dominance constraints are built on riskaverse measures for the cost functional. A suitable numerical discretization is obtained using finite elements both for the displacement and the phase field function. Different numerical experiments demonstrate the potential of the proposed stochastic shape optimization model and in particular the impact of high variability of forces or probabilities in the different realizations. 
 