15 citations · 67 across the 29 of their papers we have counts for
21 papers · 1 filter
Finite free perpetuities
Julia Le Bihan, Bartosz Kołodziejek
We introduce and study finite free perpetuities, defined as monic polynomial solutions of degree to the affine fixed-point equation \[ p(z) = \mathbb{E}\!\left[ A^{n}\,p\!\left…
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…
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 \[ \mathbb{X} \stackrel{d}{=} \mathbb{A}^{1/2}\mathbb{X}\,\mathbb{A}^{1/2} + \mathbb{B}, \]…
Perpetuities with light tails and the local dependence measure
Julia Le Bihan, Bartosz Kołodziejek
This work investigates the tail behavior of solutions to the affine stochastic fixed-point equation of the form , where and are independent. Focus…
Probability laws associated to the independence preserving quadrirational Yang-Baxter maps -- the ultimate case
Bartosz Kołodziejek, Gérard Letac, Mauro Piccioni +1
A map is said to be independence preserving (IP) if there exists a pair of independent random variables v…
Graphical Negative Multinomial and Multinomial Models with Dirichlet-type priors
Iza Danielewska, Bartosz Kołodziejek, Jacek Wesołowski +1
Bayesian statistical graphical models are typically classified as either continuous and parametric (Gaussian, parameterized by the graph-dependent precision matrix with Wishart-typ…
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…
Stochastic fixed point equation and local dependence measure
Krzysztof Burdzy, Bartosz Kołodziejek, Tvrtko Tadić
We study solutions to the stochastic fixed point equation where the coefficients and are nonnegative random variables. We introduce the ``local depen…
A renewal theorem and supremum of a perturbed random walk
Ewa Damek, Bartosz Kołodziejek
We study tails of the supremum of a perturbed random walk under regime which was not yet considered in the literature. Our approach is based on a new renewal theorem, which is of i…
Inverse Exponential Decay: Stochastic Fixed Point Equation and ARMA Models
Krzysztof Burdzy, Bartosz Kołodziejek, Tvrtko Tadić
We study solutions to the stochastic fixed point equation when the coefficients are nonnegative and is an "inverse exponential decay" (IED) random variab…
On perpetuities with light tails
Bartosz Kołodziejek
In the paper we consider the asymptotics of logarithmic tails of a perpetuity $$R \stackrel{d}{=}\sum_{j=1}^\infty Q_j \prod_{k=1}^{j-1}M_k,\qquad(M_n,Q_n)_{n=1}^\infty \mbox{ are…
A Matsumoto-Yor characterization for Kummer and Wishart random matrices
Bartosz Kołodziejek
In the paper we resolve positively the conjecture on a characterization of matrix Kummer and Wishart laws through independence property, which was posed in [Koudou, Statist. Probab…
Independence characterization for Wishart and Kummer random matrices
Agnieszka Piliszek, Bartosz Kołodziejek
We generalize the following univariate characterization of the Kummer and Gamma distributions to the cone of symmetric positive definite matrices: let and be independent, n…
The left tail of renewal measure
Bartosz Kołodziejek
In the paper, we find exact asymptotics of the left tail of renewal measure for a broad class of two-sided random walks. We only require that an exponential moment of the left tail…
Stochastic recursions: between Kesten's and Grincevičius-Grey's assumptions
Ewa Damek, Bartosz Kołodziejek
We study the stochastic recursion , where is a sequence of i.i.d. random Lipschitz mappings close to the random affine transformation $x\mapsto…
Characterization of the Riesz Exponential Family on homogeneous cones
Hideyuki Ishi, Bartosz Kołodziejek
In the paper we present a characterization theorem of the Riesz measure and a Wishart exponential family on homogeneous cones through the invariance property of a natural exponenti…
Logarithmic tails of sums of products of positive random variables bounded by one
Bartosz Kolodziejek
In this paper we show under weak assumptions that for , where and are independent copies of , we have $\ln P(R>x)\sim…
Characterization of beta distribution on symmetric cones
Bartosz Kołodziejek
In the paper we generalize the following characterization of beta distribution to the symmetric cone setting: let and be independent, non-degenerate random variables with v…
The Matsumoto--Yor Property and Its Converse on Symmetric Cones
Bartosz Kołodziejek
The Matsumoto--Yor (MY) property of the generalized inverse Gaussian and gamma distributions has many generalizations. As it was observed in (Letac and Wesołowski in Ann Probab 28:…
The Lukacs-Olkin-Rubin theorem on symmetric cones without invariance of the "quotient"
Bartosz Kołodziejek
We prove the Lukacs-Olkin-Rubin theorem without invariance of the distribution of the "quotient", which was the key assumption in the original proof of [Olkin--Rubin, Ann. Math. St…
The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem
Bartosz Kołodziejek
We prove the Lukacs characterization of the Wishart distribution on non-octonion symmetric cones of rank greater than 2. We weaken the smoothness assumptions in the version of the…