13 citations · 39 across the 22 of their papers we have counts for
26 papers
Quadratic polynomials preserving free infinite divisibility
Wiktor Ejsmont, Franz Lehner, Mihai Popa +1
We characterize non-commutative polynomials of degree 2 which preserve free infinite divisibility as self-adjoint Lie polynomials of degree 2. This extends previous results which c…
On the empirical spectral distribution of matrix perpetuities
Bartosz Kołodziejek, 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…
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 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 Perpetuities I: Existence, Subordination and Tail Asymptotics
Serban Belinschi, Bartosz Kołodziejek, Kamil Szpojankowski
We study the free analogue of the classical affine fixed-point (or perpetuity) equation \[ \mathbb{X} \stackrel{d}{=} \mathbb{A}^{1/2}\mathbb{X}\,\mathbb{A}^{1/2} + \mathbb{B}, \]…
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…
Asymptotic free independence and entry permutations for Gaussian random matrices. Part II: Infinitesimal freeness
M. Popa, K. Szpojankowski, P. -L. Tseng
We study asymptotic infinitesimal distributions of Gaussian Unitary Ensembles with permuted entries. We show that for random uniform permutations, the asymptotically permuted GUE m…
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…
A phase transition for tails of the free multiplicative convolution powers
Bartosz Kołodziejek, Kamil Szpojankowski
We study the behavior of the tail of a measure , where is the -fold free multiplicative convolution power for . We focus on the case wher…
Asymptotic --distribution of permuted Haar unitary matrices
James A. Mingo, Mihai Popa, Kamil Szpojankowski
We study Haar unitary random matrices with permuted entries. For a sequence of permutations , where acts on matrices we identify conditions un…
Using Boolean cumulants to study multiplication and anticommutators of free random variables
Maxime Fevrier, Mitja Mastnak, Alexandru Nica +1
We study how Boolean cumulants can be used in order to address operations with freely independent random variables, particularly in connection to the -distribution of the produc…
Boolean Cumulants and Subordination in Free Probability
Franz Lehner, Kamil Szpojankowski
We study subordination of free convolutions. We prove that for free random variables and a Borel function the conditional expectation $E_φ\left[ (z-X-f(X)Yf^*(X))^{-1}| X…
Conditional expectations through Boolean cumulants and subordination -- towards a better understanding of the Lukacs property in free probability
Kamil Szpojankowski, Jacek Wesołowski
We use here a recent idea of studying functions of free random variables using Boolean cumulants. We develop idea of explicit calculations of conditional expectation using Boolean…
A construction which relates c-freeness to infinitesimal freeness
Maxime Fevrier, Mitja Mastnak, Alexandru Nica +1
We consider two extensions of free probability that have been studied in the research literature, and are based on the notions of c-freeness and respectively of infinitesimal freen…
On free Generalized Inverse Gaussian distributions
Takahiro Hasebe, Kamil Szpojankowski
We study here properties of free Generalized Inverse Gaussian distributions (fGIG) in free probability. We show that in many cases the fGIG shares similar properties with the class…
Quantum Bernstein's Theorem and the Hyperoctahedral Quantum Group
Paweł Józiak, Kamil Szpojankowski
We study an extension of Bernstein's theorem to the setting of quantum groups. For a d-tuple of free, identically distributed random variables we consider a problem of preservation…
Eta-diagonal distributions and infinite divisibility for R-diagonals
Hari Bercovici, Alexandru Nica, Michael Noyes +1
The class of R-diagonal *-distributions is fairly well understood in free probability. In this class, we consider the concept of infinite divisibility with respect to the operation…
On the Matsumoto-Yor property in free probability
Kamil Szpojankowski
We study the Matsumoto-Yor property in free probability. We prove that the limiting empirical eigenvalue distribution of the GIG matrices and the Marchenko-Pastur distribution have…
Convolution, subordination and characterization problems in noncommutative probability
Wiktor Ejsmont, Uwe Franz, Kamil Szpojankowski
Characterization problems in free probability are studied here. Using subordination of free additive and free multiplicative convolutions we generalize some known characterizations…
A constant regression characterization of a Marchenko-Pastur law
Kamil Szpojankowski
Lukacs type characterization of Marchenko--Pastur distribution in free probability is studied here. We prove that for free and when conditional moments of…
On the Lukacs property for free random variables
Kamil Szpojankowski
The Lukacs property of the free Poisson distribution is studied here. We prove that if free $\X$ and $\Y$ are free Poisson distributed with suitable parameters, then $\X+\Y$ and $\…