 2017Kaveh Bashiri
A note on the metastability in three modifications of the standard Ising model
2017
https://arxiv.org/pdf/1705.07012.pdf

 
 Anton Bovier, Loren Coquille and Rebecca Neukirch
The recovery of a recessive allele in a Mendelian dipoloid model
2017
https://arxiv.org/abs/1703.02459

 
 S. Chhita, P.L. Ferrari and F.L. Toninelli
Speed and fluctuations for some driven dimer models
preprint: arXiv:1705.07641 2017
https://arxiv.org/abs/1705.07641
Abstract: We consider driven dimer models on the square and honeycomb graphs, starting from a stationary Gibbs measure. Each model can be thought of as a two dimensional stochastic growth model of an interface, belonging to the anisotropic KPZ universality class. We use a combinatorial approach to determine the speed of growth and show logarithmic growth in time of the variance of the height function fluctuations. 
 
 S. Conti, M. Klar and B. Zwicknagl
Piecewise affine stressfree martensitic inclusions in planar nonlinear elasticity
Proc. Roy. Soc. A, 473(2203) 2017
http://rspa.royalsocietypublishing.org/content/473/2203/20170235
Abstract: We consider a partial differential inclusion problem which models stressfree martensitic inclusions in an austenitic matrix, based on the standard geometrically nonlinear elasticity theory. We show that for specific parameter choices there exist piecewise affine continuous solutions for the squaretooblique and the hexagonaltooblique phase transitions. This suggests that for specific crystallographic parameters the hysteresis of the phase transformation will be particularly small. 
 
 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. 
 
 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. 
 
 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

 