8 papers · 1 filter
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 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…
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 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…
Free Integral Calculus I
Franz Lehner, Kamil Szpojankowski
We study the problem of conditional expectations in free random variables and provide closed formulas for the conditional expectation of resolvents of arbitrary non-commutative pol…
On the Partial Transpose of a Haar Unitary Matrix
James A. Mingo, Mihai Popa, Kamil Szpojankowski
We consider the effect of a partial transpose on the limit -distribution of a Haar distributed random unitary matrix. If we fix, , the number of blocks, we show that the part…