Publications of Matthias Ernst Sachs    :chronological  alphabetical  combined listing:

%% Papers Published   
@article{fds350396,
   Author = {Lu, J and Sachs, M and Steinerberger, S},
   Title = {Quadrature Points via Heat Kernel Repulsion},
   Journal = {Constructive Approximation},
   Volume = {51},
   Number = {1},
   Pages = {27-48},
   Year = {2020},
   Month = {February},
   url = {http://dx.doi.org/10.1007/s00365-019-09471-4},
   Abstract = {© 2019, Springer Science+Business Media, LLC, part of
             Springer Nature. We discuss the classical problem of how to
             pick N weighted points on a d-dimensional manifold so as to
             obtain a reasonable quadrature rule 1|M|∫Mf(x)dx≃∑n=1Naif(xi).This
             problem, naturally, has a long history; the purpose of our
             paper is to propose selecting points and weights so as to
             minimize the energy functional ∑i,j=1Naiajexp(-d(xi,xj)24t)→min,wheret∼N-2/d,d(x, y)
             is the geodesic distance, and d is the dimension of the
             manifold. This yields point sets that are theoretically
             guaranteed, via spectral theoretic properties of the
             Laplacian - Δ , to have good properties. One nice aspect is
             that the energy functional is universal and independent of
             the underlying manifold; we show several numerical
             examples.},
   Doi = {10.1007/s00365-019-09471-4},
   Key = {fds350396}
}

@article{fds350397,
   Author = {Leimkuhler, B and Sachs, M and Stoltz, G},
   Title = {Hypocoercivity Properties of Adaptive Langevin
             Dynamics},
   Journal = {Siam Journal on Applied Mathematics},
   Volume = {80},
   Number = {3},
   Pages = {1197-1222},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {2020},
   Month = {January},
   url = {http://dx.doi.org/10.1137/19m1291649},
   Doi = {10.1137/19m1291649},
   Key = {fds350397}
}

@article{fds350398,
   Author = {Leimkuhler, B and Sachs, M},
   Title = {Ergodic Properties of Quasi-Markovian Generalized Langevin
             Equations with Configuration Dependent Noise and
             Non-conservative Force},
   Pages = {282-330},
   Publisher = {Springer International Publishing},
   Editor = {Giacomin, G and Olla, S and Saada, E and Spohn, H and Stoltz,
             G},
   Year = {2019},
   Abstract = {We discuss the ergodic properties of quasi-Markovian
             stochastic differential equations, providing general
             conditions that ensure existence and uniqueness of a smooth
             invariant distribution and exponential convergence of the
             evolution operator in suitably weighted $$L^\infty $$spaces,
             which implies the validity of central limit theorem for the
             respective solution processes. The main new result is an
             ergodicity condition for the generalized Langevin equation
             with configuration-dependent noise and (non-)conservative
             force.},
   Key = {fds350398}
}


%% Other   
@misc{fds350399,
   Author = {Sachs, ME},
   Title = {Generalised Langevin equation: asymptotic properties and
             numerical analysis},
   Year = {2018},
   Key = {fds350399}
}