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pro vyhledávání: '"Maas, Jan"'
We prove upper bounds on the $L^\infty$-Wasserstein distance from optimal transport between strongly log-concave probability densities and log-Lipschitz perturbations. In the simplest setting, such a bound amounts to a transport-information inequalit
Externí odkaz:
http://arxiv.org/abs/2402.04151
Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time $T_1$ by adding noise to the data, (ii) estimate its score function, and (iii) use such
Externí odkaz:
http://arxiv.org/abs/2305.14164
Publikováno v:
Tran. Amer. Math. Soc. 2024 (online)
This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical Kurdyka--{\
Externí odkaz:
http://arxiv.org/abs/2304.05239
Autor:
Brooks, Morris, Maas, Jan
Let $X$ be a vector field and $Y$ be a co-vector field on a smooth manifold $M$. Does there exist a smooth Riemannian metric $g_{\alpha \beta}$ on $M$ such that $Y_\beta = g_{\alpha \beta} X^\alpha$? The main result of this note gives necessary and s
Externí odkaz:
http://arxiv.org/abs/2209.11149
This paper deals with the large-scale behaviour of dynamical optimal transport on $\mathbb{Z}^d$-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes the effect
Externí odkaz:
http://arxiv.org/abs/2110.15321
This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou-Brenier formula for the Wasserstein distance, which establishes the equivalence of static and dynamical optimal transport. Secondly,
Externí odkaz:
http://arxiv.org/abs/2105.05677
We consider finite-volume approximations of Fokker-Planck equations on bounded convex domains in $\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker-Planck equation via
Externí odkaz:
http://arxiv.org/abs/2008.10962
We study the temporal dissipation of variance and relative entropy for ergodic Markov Chains in continuous time, and compute explicitly the corresponding dissipation rates. These are identified, as is well known, in the case of the variance in terms
Externí odkaz:
http://arxiv.org/abs/2005.14177
Autor:
Maas, Jan, Mielke, Alexander
We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the micro
Externí odkaz:
http://arxiv.org/abs/2004.02831