Anton Bovier and Lisa B. Hartung Extended Convergence of the Extremal Process of Branching Brownian Motion ArXiv e-prints 2014 http://arxiv.org/abs/1412.5975
Abstract: We extend the results of Arguin et al and A\"\i{}d\'ekon et al on the convergence of the extremal process of branching Brownian motion by adding an extra dimension that encodes the "location" of the particle in the underlying Galton-Watson tree. We show that the limit is a cluster point process on R+×R where each cluster is the atom of a Poisson point process on R+×R with a random intensity measure Z(dz)×Ce−2√x, where the random measure is explicitly constructed from the derivative martingale. This work is motivated by an analogous conjecture for the Gaussian free field by Biskup and Louidor.
2013
Benjamin Berkels, Tom Fletcher, Behrend Heeren, Martin Rumpf and Benedikt Wirth Discrete geodesic regression in shape space In Anders Heyden, Fredrik Kahl, Carl Olsson, Magnus Oskarsson, Xue-Cheng Tai, editor, Energy Minimization Methods in Computer Vision and Pattern Recognition, Volume 8081 of Lecture Notes in Computer Science
page 108-122.
Publisher: Springer International
2013 http://dx.doi.org/10.1007/978-3-642-40395-8_9
Abstract: A new approach for the effective computation of geodesic re- gression curves in shape spaces is presented. Here, one asks for a geodesic curve on the shape manifold that minimizes a sum of dissimilarity mea- sures between given two- or three-dimensional input shapes and corre- sponding shapes along the regression curve. The proposed method is based on a variational time discretization of geodesics. Curves in shape space are represented as deformations of suitable reference shapes, which renders the computation of a discrete geodesic as a PDE constrained optimization for a family of deformations. The PDE constraint is de- duced from the discretization of the covariant derivative of the velocity in the tangential direction along a geodesic. Finite elements are used for the spatial discretization, and a hierarchical minimization strategy together with a Lagrangian multiplier type gradient descent scheme is implemented. The method is applied to the analysis of root growth in botany and the morphological changes of brain structures due to aging.
Sven Beuchler, Veronika Pillwein and Sabine Zaglmayr Sparsity optimized high order finite element functions for $H(\romancurl)$ on tetrahedra Adv. in Appl. Math., 50(5): 749--769 2013 http://dx.doi.org/10.1016/j.aam.2012.11.004
Sven Beuchler, Veronika Pillwein and Sabine Zaglmayr Fast summation techniques for sparse shape functions in tetrahedral $hp$-FEM In Domain decomposition methods in science and engineering {XX}, Volume 91 of Lect. Notes Comput. Sci. Eng.
page 511--518.
Publisher: Springer, Heidelberg
2013 http://dx.doi.org/10.1007/978-3-642-35275-1_60
2012
Sven Beuchler, Veronika Pillwein, Joachim Schöberl and Sabine Zaglmayr Sparsity optimized high order finite element functions on simplices In Numerical and symbolic scientific computing, Texts Monogr. Symbol. Comput.
page 21--44.
Publisher: SpringerWienNewYork, Vienna
2012 http://dx.doi.org/10.1007/978-3-7091-0794-2_2
0
A. Borodin, I. Corwin and P.L. Ferrari Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes preprint, arXiv:1612.00321 0 http://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 q-Whittaker 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 space-time limit to the (2+1)-dimensional additive stochastic heat equation (or Edwards-Wilkinson equation) along characteristic directions. In particular, the bulk height function converges to the Gaussian free field which evolves according to this stochastic PDE.
A. Borodin, A. Bufetov and P.L. Ferrari TASEP with a moving wall preprint: arXiv:2111.02530 0 http://arxiv.org/abs/2111.02530
Abstract: We consider a totally asymmetric simple exclusion on Z with the step initial condition, under the additional restriction that the first particle cannot cross a deterministally moving wall. We prove that such a wall may induce asymptotic fluctuation distributions of particle positions of the form P(supÏâR{Airy2(Ï)âg(Ï)}â¤S) with arbitrary barrier functions g. This is the same class of distributions that arises as one-point asymptotic fluctuations of TASEPs with arbitrary initial conditions. Examples include Tracy-Widom GOE and GUE distributions, as well as a crossover between them, all arising from various particles behind a linearly moving wall. We also prove that if the right-most particle is second class, and a linearly moving wall is shock-inducing, then the asymptotic distribution of the position of the second class particle is a mixture of the uniform distribution on a segment and the atomic measure at its right end.
Anton Bovier From spin glasses to branching Brownian motion---and back? In Random walks, random fields, and disordered systems, Volume 2144 of Lecture Notes in Math.
page 1--64.
Publisher: Springer, Cham
0 http://dx.doi.org/10.1007/978-3-319-19339-7_1