9 papers
On the empirical spectral distribution of matrix perpetuities
Bartosz KoÅodziejek, Kamil Szpojankowski
We study matrix perpetuities, that is, solutions to affine fixed-point equations of the form \[ \mathbf{X} \stackrel{d}{=} \mathbf{A}\,\mathbf{X} \,\mathbf{A}^\top+\mathbf{B},\qqua…
On the Brown measure of , with selfadjoint and free Poisson
Franz Lehner, Alexandru Nica, Kamil Szpojankowski +1
Let be freely independent selfadjoint elements in a -probability space, where has free Poisson distribution of parameter . We pursue a methodology for computing…
Polynomials in -free random variables with applications to free denoising
Adrian Celestino, Franz Lehner, Kamil Szpojankowski
We study distributions of polynomials in conditionally free (c-free) random variables, a notion of independence for two-state noncommutative probability spaces introduced by Bozejk…
On some properties of free commutators with semicircular variables
Mihai Popa, Kamil Szpojankowski
We investigate commutators of free variables of the form \( i[x, s] \), where \( s \) is a semicircular element. We show that although \( s \) and \( i[x, s] \) are not free, their…
Free Askey--Wilson functionals and geometric last passage percolation on a strip
Wlodek Bryc, Kamil Szpojankowski, Jacek Wesolowski
Barraquand, Corwin, and Yang arXiv:2306.05983 established that geometric last passage percolation (LPP) on a strip of has a unique stationary measure. Building on th…
Free denoising via overlap measures and c-freeness techniques
Maxime Fevrier, Alexandru Nica, Kamil Szpojankowski
We study the problem of free denoising. For free selfadjoint random variables , where we interpret as a signal and as noise, we find . To that end, we study…