85 citations · 253 across the 31 of their papers we have counts for
40 papers
Sharp estimates for the Opdam-Cherednik -invariant heat kernel for the root system
Piotr Graczyk, Patrice Sawyer
For the first time, the estimates of the non-centered Weyl-group invariant heat kernel for curved Riemannian spaces and for Opdam-Cherednik Laplacians are studied systematically. W…
Graphical Gaussian models associated to a homogeneous graph with permutation symmetries
Piotr Graczyk, Hideyuki Ishi, Bartosz Kołodziejek
We consider multivariate centered Gaussian models for the random vector , whose conditional structure is described by a homogeneous graph and which is invariant…
Sharp estimates for the hypergeometric functions related to root systems of type and of rank 1
Piotr Graczyk, Patrice Sawyer
In this article, we conjecture exact estimates for the Weyl-invariant Opdam-Cherednik hypergeometric functions. We prove the conjecture for the root system and for all rank 1…
Pattern recovery by SLOPE
Małgorzata Bogdan, Xavier Dupuis, Piotr Graczyk +4
SLOPE is a popular method for dimensionality reduction in the high-dimensional regression. Indeed some regression coefficient estimates of SLOPE can be null (sparsity) or can be eq…
Pattern recovery and signal denoising by SLOPE when the design matrix is orthogonal
Tomasz Skalski, Piotr Graczyk, Bartosz Kołodziejek +1
Sorted Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows to reduce the model dimens…
Sharp estimates for -invariant Dunkl and heat kernels in the case
Piotr Graczyk, Patrice Sawyer
In this article, we prove exact estimates for the -invariant Dunkl kernel and heat kernel, for the root system of type with arbitrary positive multiplicities. We apply the e…