 2016A. 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. 
 
 Sergio Conti and Michael Ortiz
Optimal Scaling in Solids Undergoing Ductile Fracture by Crazing
Arch. Rat. Mech. Anal., 219(2): 607636 2016
http://dx.doi.org/10.1007/s002050150901y
Abstract: We derive optimal scaling laws for the macroscopic fracture energy of polymers failing by crazing. We assume that the effective deformationtheoretical freeenergy density is additive in the first and fractional deformationgradients, with zero growth in the former and linear growth in the latter. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. For this particular geometry, we derive optimal scaling laws for the dependence of the specific fracture energy on crosssectional area, micromechanical parameters, opening displacement and intrinsic length of the material. In particular, the upper bound is obtained by means of a construction of the crazing type. 
 
 P.L. Ferrari and P. Nejjar
Fluctuations of the competition interface in presence of shocks
arXiv:1603.07498 2016
http://arxiv.org/abs/1603.07498
Abstract: We consider last passage percolation (LPP) models with exponentially distributed random variables, which are linked to the totally asymmetric simple exclusion process (TASEP). The competition interface for LPP was introduced and studied by Ferrari and Pimentel in [Ann. Probab. 33 (2005), 12351254] for cases where the corresponding exclusion process had a rarefaction fan. Here we consider situations with a shock and determine the law of the fluctuations of the competition interface around its deterministic law of large number position. We also study the multipoint distribution of the LPP around the shock, extending our onepoint result of [Probab. Theory Relat. Fields 61 (2015), 61109]. 
 
 P.L. Ferrari and H. Spohn
On time correlations for KPZ growth in one dimension
preprint: arXiv:1602.00486 2016
http://arxiv.org/abs/1602.00486
Abstract: Time correlations for KPZ growth in 1+1 dimensions are reconsidered. We discuss flat, curved, and stationary initial conditions and are interested in the covariance of the height as a function of time at a fixed point on the substrate. In each case the power laws of the covariance for short and long times are obtained. They are derived from a variational problem involving two independent Airy processes. For stationary initial conditions we derive an exact formula for the stationary covariance with two approaches: (1) the variational problem and (2) deriving the covariance of the timeintegrated current at the origin for the corresponding driven lattice gas. In the stationary case we also derive the large time behavior for the covariance of the height gradients. 
 
 P.L. Ferrari and B. Vető
The hardedge tacnode process for Brownian motion
preprint, arXiv:1608.00394 2016
https://arxiv.org/abs/1608.00394
Abstract: {We consider N nonintersecting Brownian bridges conditioned to stay below a fixed threshold. We consider a scaling limit where the limit shape is tangential to the threshold. In the large N limit, we determine the limiting distribution of the top Brownian bridge conditioned to stay below a function as well as the limiting correlation kernel of the system. It is a oneparameter family of processes which depends on the tuning of the threshold position on the natural fluctuation scale. We also discuss the relation to the sixvertex model and the Aztec diamond on restricted domains.} 
 
 Michael Herrmann, Barbara Niethammer and Juan J. L. Velázquez
Instabilities and oscillations in coagulation equations with kernels of homogeneity one
2016
http://arxiv.org/abs/1606.09405

 
 Richard Höfer and Juan JL Velázquez
The Method of Reflections, Homogenization and Screening for Poisson and Stokes Equations in Perforated Domains
2016
http://arxiv.org/abs/1603.06750

 
 Peter Hornung, Martin Rumpf and Stefan Simon
Material Optimization for Nonlinearly Elastic Planar Beams
2016
http://arxiv.org/abs/1604.02267

 
 A.H.M. Kierkels
On a kinetic equation in weak turbulence theory for the nonlinear Schrödinger equation
2016
http://arxiv.org/abs/1606.07290

 
 Herbert Koch, Angkana Rüland and Wenhui Shi
The variable coefficient thin obstacle problem: Carleman inequalities
Adv. Math., 301: 820866 2016
http://dx.doi.org/10.1016/j.aim.2016.06.023

 
 P. Laurençot, B. Niethammer and J. J. L. Velázquez
Oscillatory dynamics in Smoluchowski's coagulation equation with diagonal kernel
2016
http://arxiv.org/abs/1603.02929

 
 Jan Maas, Martin Rumpf and Stefan Simon
Generalized optimal transport with singular sources
2016
http://arxiv.org/abs/1607.01186

 
 Patrick Müller
Path large deviations for interacting diffusions with local meanfield interactions
2016
http://arxiv.org/abs/1512.05323
Abstract: We consider a system of Nd spins, with a local mean field type interaction. Each spin has a fixed spacial position on the torus Td and a spin value in R that evolves according to a space dependent Langevin dynamic. The interaction between two spins depends on their spacial distance. We investigate the path large deviation principle from the hydrodynamic (or local mean field McKeanVlasov) limit and characterise the rate function, for both the space dependent empirical process and the space dependent empirical measure of the paths. To this end, we generalize an approach of Dawson and G\"artner. By the space dependency, this requires new ingredients compared to mean field type interactions. Moreover, we prove the large deviation principle by using second approach. This requires a generalisation of Varadhan's lemma to nowhere continuous functions. 
 
 A. Nota and J.J.L. Velázquez
On the growth of a particle coalescing in a Poisson distribution of obstacles
2016
http://arxiv.org/abs/1608.08118

 
 Alan D. Rendall and Juan J. L. Velázquez
Veiled singularities for the spherically symmetric massless EinsteinVlasov system
2016
http://arxiv.org/abs/1604.06576

 
 Angkana Rüland, Christian Zillinger and Barbara Zwicknagl
Higher Sobolev regularity of convex integration solutions in elasticity
2016
https://arxiv.org/abs/1610.02529

 
 2015Sebastian Andres and Naotaka Kajino
Continuity and estimates for the Liouville heat kernel with applications to spectral dimensions
Probab. Theory Relat. Fields 2015
http://dx.doi.org/10.1007/s0044001506704

 
 Sebastian Andres, JeanDominique Deuschel and Martin Slowik
Harnack inequalities on weighted graphs and some applications to the random conductance model
Probab. Theory Relat. Fields: 147 2015
http://dx.doi.org/10.1007/s004400150623y
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. 
 