From the 1 of 6 linked papers with an AI index.
6 papers
Singularities of matrix semicircles
Vladislav Kargin
The paper studies matrix semicircular elements whose spectral density becomes singular at zero, classifying the singular behavior for binary Hermitian pencils and showing how the l…
Free compressions of R-diagonal random variables and the semigroup of Brown measures
Vladislav Kargin
We investigate the Brown measures of compressions of -diagonal random variables, extending previous results to include unbounded cases. For random variables with finite variance…
Lecture Notes on Free Probability
Vladislav Kargin
These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness,…
The smallest singular value of large random rectangular Toeplitz and circulant matrices
Alexei Onatski, Vladislav Kargin
Let , be a sequence of i.i.d. standard normal random variables. Consider rectangular Toeplitz …
On the joint distribution of the area and the number of peaks for Bernoulli excursions
Vladislav Kargin
Let be a random Bernoulli excursion of length . We show that the area under and the number of peaks of are asymptotically independent. We also show that these…
An upper bound on the per-tile entropy of ribbon tilings
Simon Blackburn, Yinsong Chen, Vladislav Kargin
This paper considers -ribbon tilings of general regions and their per-tile entropy (the binary logarithm of the number of tilings divided by the number of tiles). We show that t…