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pro vyhledávání: '"Sambale, Holger"'
Consider a stationary Poisson process $\eta$ in the $d$-dimensional Euclidean or hyperbolic space and construct a random graph with vertex set $\eta$ as follows. First, each point $x\in\eta$ is connected by an edge to its nearest neighbour, then to i
Externí odkaz:
http://arxiv.org/abs/2411.00748
Autor:
Götze, Friedrich, Sambale, Holger
We study various generalizations of concentration of measure on the unit sphere, in particular by means of log-Sobolev inequalities. First, we show Sudakov-type concentration results and local semicircular laws for weighted random matrices. A further
Externí odkaz:
http://arxiv.org/abs/2408.04346
Autor:
Buterus, Paul, Sambale, Holger
We investigate the relation between moments and tails of heavy-tailed (in particular, Pareto-type) distributions. We also discuss the sharpness of our results in a number of examples under certain regularity conditions like log-convexity. Moreover, w
Externí odkaz:
http://arxiv.org/abs/2308.14410
Autor:
Götze, Friedrich, Sambale, Holger
We prove higher order concentration bounds for functions on Stiefel and Grassmann manifolds equipped with the uniform distribution. This partially extends previous work for functions on the unit sphere. Technically, our results are based on logarithm
Externí odkaz:
http://arxiv.org/abs/2208.07641
Sequences of discrete random variables are studied whose probability generating functions are zero-free in a sector of the complex plane around the positive real axis. Sharp bounds on the cumulants of all orders are stated, leading to Berry-Esseen bo
Externí odkaz:
http://arxiv.org/abs/2207.08469
We consider products of uniform random variables from the Stiefel manifold of orthonormal $k$-frames in $\mathbb{R}^n$, $k \le n$, and random vectors from the $n$-dimensional $\ell_p^n$-ball $\mathbb{B}_p^n$ with certain $p$-radial distributions, $p\
Externí odkaz:
http://arxiv.org/abs/2203.00476
In this note we study the block spin mean-field Potts model, in which the spins are divided into $s$ blocks and can take $q\ge 2$ different values (colors). Each block is allowed to contain a different proportion of vertices and behaves itself like a
Externí odkaz:
http://arxiv.org/abs/2103.16421
Autor:
Sambale, Holger, Sinulis, Arthur
We present concentration inequalities on the multislice which are based on (modified) log-Sobolev inequalities. This includes bounds for convex functions and multilinear polynomials. As an application we show concentration results for the triangle co
Externí odkaz:
http://arxiv.org/abs/2010.16289
We introduce and analyze a generalization of the blocks spin Ising (Curie-Weiss) models that were discussed in a number of recent articles. In these block spin models each spin in one of $s$ blocks can take one of a finite number of $q \ge 3$ values,
Externí odkaz:
http://arxiv.org/abs/2010.15542
Publikováno v:
Stochastic Processes and their Applications, vol. 140, pp. 216-235 (2021)
Concentration properties of functionals of general Poisson processes are studied. Using a modified $\Phi$-Sobolev inequality a recursion scheme for moments is established, which is of independent interest. This is applied to derive moment and concent
Externí odkaz:
http://arxiv.org/abs/2009.00316