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- Zdzisław Burda, Jakub Duda, Jean-Marc Luck, Bartłomiej Waclaw
- Physical review letters
- 2009

We define a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic random walk if it takes place on a regular lattice, but it is not if… (More)

- Zdzisław Burda, Jerzy Jurkiewicz, A. Krzywicki
- Physical review. E, Statistical, nonlinear, and…
- 2004

This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical… (More)

- Zdzisław Burda, Andrzej Jarosz, Giacomo Livan, Maciej A. Nowak, Artur Swiech
- Physical review. E, Statistical, nonlinear, and…
- 2010

We derive exact analytic expressions for the distributions of eigenvalues and singular values for the product of an arbitrary number of independent rectangular gaussian random matrices in the limit… (More)

- Zdzisław Burda, A. Krzywicki, Olivier C. Martin, Marcin Zagórski
- Proceedings of the National Academy of Sciences…
- 2011

Gene regulatory networks allow the control of gene expression patterns in living cells. The study of network topology has revealed that certain subgraphs of interactions or "motifs" appear at… (More)

- Zdzisław Burda, Jerzy Jurkiewicz, Bartłomiej Wacław
- Physical review. E, Statistical, nonlinear, and…
- 2005

We present an analytic method to determine the spectral properties of the covariance matrices constructed of correlated Wishart random matrices. The method gives, in the limit of large matrices,… (More)

- Zdzisław Burda, A. Krzywicki, Olivier C. Martin, Marcin Zagórski
- Physical review. E, Statistical, nonlinear, and…
- 2010

Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. They also tend to have broad distributions for the out-degree. What… (More)

- Zdzisław Burda, Romuald A. Janik, Bartłomiej Waclaw
- Physical review. E, Statistical, nonlinear, and…
- 2010

We show that the eigenvalue density of a product X=X1X2...XM of M independent NxN Gaussian random matrices in the limit N-->infinity is rotationally symmetric in the complex plane and is given by a… (More)

- Zdzisław Burda, Jerzy Jurkiewicz, Maciej A. Nowak, Gabor Papp, Ismail Zahed
- Physical review. E, Statistical, nonlinear, and…
- 2007

We compare eigenvalue densities of Wigner random matrices whose elements are independent identically distributed random numbers with a Lévy distribution and maximally random matrices with a… (More)

- Zdzisław Burda, Jerzy Jurkiewicz, A. Krzywicki
- Physical review. E, Statistical, nonlinear, and…
- 2004

This paper is a direct continuation of an earlier work, where we studied Erdös-Rényi random graphs perturbed by an interaction Hamiltonian favoring the formation of short cycles. Here, we generalize… (More)

- Zdzisław Burda, A. Krzywicki, Olivier C. Martin
- Physical review. E, Statistical, nonlinear, and…
- 2008

Multiagent models have been used in many contexts to study generic collective behavior. Similarly, complex networks have become very popular because of the diversity of growth rules giving rise to… (More)