[Show abstract][Hide abstract] ABSTRACT: We prove the "strong conjecture" expressed by Gazeau et al. in
arXiv:1203.3936v1 [math-ph] about the coefficients of the Taylor expansion of
the exponential of a polynomial. This implies the "weak conjecture" as a
special case. The proof relies mainly about properties of the Gould-Hopper
Journal of Mathematical Physics 03/2012; 54(7). · 1.30 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this paper, we show that the sum rules for generalized Hermite polynomials derived by Daboul and Mizrahi (2005 J. Phys. A: Math. Gen. http://dx.doi.org/10.1088/0305-4470/38/2/010) and by Graczyk and Nowak (2004 C. R. Acad. Sci., Ser. 1 338 849) can be interpreted and easily recovered using a probabilistic moment representation of these polynomials. The covariance property of the raising operator of the harmonic oscillator, which is at the origin of the identities proved in Daboul and Mizrahi and the dimension reduction effect expressed in the main result of Graczyk and Nowak are both interpreted in terms of the rotational invariance of the Gaussian distributions. As an application of these results, we uncover a probabilistic moment interpretation of two classical integrals of the Wigner function that involve the associated Laguerre polynomials.
Journal of Physics A Mathematical and Theoretical 11/2011; 45(1):015001. · 1.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We show that various identities from  and  involving Gould-Hopper
polynomials can be deduced from the real but also complex orthogonal invariance
of multivariate Gaussian distributions. We also deduce from this principle a
useful stochastic representation for the inner product of two non-centered
Gaussian vectors and two non-centered Gaussian matrices.  J. Daboul, S. S.
Mizrahi, O(N) symmetries, sum rules for generalized Hermite polynomials and
squeezed state, J. Phys. A: Math. Gen. 38 (2005) 427-448  P. Graczyk, A.
Nowak, A composition formula for squares of Hermite polynomials and its
generalizations, C. R. Acad. Sci. Paris, Ser 1 338 (2004)
[Show abstract][Hide abstract] ABSTRACT: Ocean currents, prevailing winds, and the hierarchical structures of river networks are known to create asymmetries in re-colonization between habitat patches. The impacts of such asymmetries on metapopulation persistence are seldom considered, especially rarely in theoretical studies. Considering three classical models (the island, the stepping stone and the distance-dependent model), we explore how metapopulation persistence is affected by (i) asymmetry in dispersal strength, in which the colonization rate between two patches differs in direction, and (ii) asymmetry in connectivity, in which the overall colonization pattern displays asymmetry (circulating or dendritic networks). Viability can be drastically reduced when directional bias in dispersal strength is higher than 25%. Re-colonization patterns that allow for strong local connectivity provide the highest persistence compared to systems that allow circulation. Finally, asymmetry has relatively weak effects when metapopulations maintain strong general connectivity.
Theoretical Population Biology 11/2010; 78(3):225-38. · 1.24 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The flip-and-forward scheme introduced in (Yang-Belfiore, 2007) for handling communication in multi-hop MIMO relay networks was shown to achieve a better diversity-multiplexing tradeoff than pure amplify-and-forward schemes. In the present paper, we show that the flip-and-forward scheme actually achieves the optimal diversity-multiplexing tradeoff for a two-hop relay network, when the relay is equipped with two antennas.
Cognitive Radio Oriented Wireless Networks & Communications (CROWNCOM), 2010 Proceedings of the Fifth International Conference on; 07/2010
[Show abstract][Hide abstract] ABSTRACT: We investigate the role of cooperation in wireless networks subject to a spatial degrees of freedom limitation. To address the worst case scenario, we consider a free-space line-of-sight type environment with no scattering and no fading. We identify three qualitatively different operating regimes that are determined by how the area of the network A, normalized with respect to the wavelength Â¿, compares to the number of users n. In networks with Â¿A/Â¿ Â¿ Â¿n, the limitation in spatial degrees of freedom does not allow to achieve a capacity scaling better than Â¿n and this performance can be readily achieved by multi-hopping. This result has been recently shown in . However, for networks with Â¿A/Â¿ > Â¿n the number of available degrees of freedom is min (n, Â¿A/Â¿), larger that what can be achieved by multi-hopping. We show that the optimal capacity scaling in this regime is achieved by hierarchical cooperation. In particular, in networks with Â¿A/Â¿ > n, hierarchical cooperation can achieve linear scaling.
Information Theory and Applications Workshop (ITA), 2010; 03/2010
[Show abstract][Hide abstract] ABSTRACT: The rotate-and-forward scheme was introduced in (Yang-Belfiore, 2010) to recover spatial diversity in multi-hop MIMO relay networks. It was shown that this scheme achieves the optimal diversity-multiplexing (DMT) trade-off in a two-hop relay network, with two antennas at the relay node. In this paper, it is shown that the scheme is DMT optimal for arbitrary number of antennas at the source, relay, and destination node.
Proceedings of Allerton Conference on Communication, Control and Computing. 01/2010;
[Show abstract][Hide abstract] ABSTRACT: The rate region achievable by two transmitter-receiver pairs who wish to communicate over a Gaussian interference channel has been the subject of intense study over the last decades. Recently, the high SNR capacity region of this channel has been completely characterized in a work by Etkin, Tse and Wang (2007). In this paper, we study the effect of adding random fading into the picture, as well as multiple antennas at the transmitters and the receivers. Under the fast fading assumption, we recover a result of the same type as that obtained in the above mentioned paper. Under the slow fading assumption, we obtain an upper bound on the maximally achievable diversity order for a given target rate pair, which we conjecture to be tight.
Information Theory, 2008. ISIT 2008. IEEE International Symposium on; 08/2008
[Show abstract][Hide abstract] ABSTRACT: We establish the high SNR diversity-multiplexing tradeoff of the fading interference channel, for a general interference level and under the assumption that transmitters and receivers are equipped with a single antenna each.
Communications, 2008 IEEE International Zurich Seminar on; 04/2008
[Show abstract][Hide abstract] ABSTRACT: The capacity scaling of extended two-dimensional wireless networks is known in the high-attenuation regime, i.e., when the power path loss exponent alpha is greater than 4. This has been accomplished by deriving information-theoretic upper bounds for this regime that match the corresponding lower bounds. On the contrary, not much is known in the so-called low-attenuation regime when 2lesalphales4. (For one-dimensional networks, the uncharacterized regime is 1lesalphales2.5.) The dichotomy is due to the fact that while communication is highly power-limited in the first case and power-based arguments suffice to get tight upper bounds, the study of the low-attenuation regime requires a more precise analysis of the degrees of freedom involved. In this paper, we study the capacity scaling of extended wireless networks with an emphasis on the low-attenuation regime and show that in the absence of small scale fading, the low attenuation regime does not behave significantly different from the high attenuation regime.
IEEE Transactions on Information Theory 11/2007; · 2.62 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This paper analyzes the capacity of a wireless relay network composed of a large number of nodes that operate in an amplify-and-forward mode and that divide into a fixed number of levels. The capacity computation relies on the study of products of large random matrices, whose limiting eigenvalue distribution is computed via a set of recursive equations.
Information Theory, 2007. ISIT 2007. IEEE International Symposium on; 07/2007
[Show abstract][Hide abstract] ABSTRACT: We derive an information theoretic scaling law for the maximum achievable rate per communication pair in a two-dimensional random ad-hoc wireless network. Our scaling law holds for non-absorptive media and when the path loss exponent (describing the decay of the amplitude of the signal) is between 1 and 2. The key ingredient of our result is the recently established information theoretic scaling law for one-dimensional ad-hoc wireless networks in the attenuation regime of interest
Communications, 2006 International Zurich Seminar on; 02/2006
[Show abstract][Hide abstract] ABSTRACT: We obtain a precise information-theoretic upper bound on the rate per communication pair in a one-dimensional ad hoc wireless network. The key ingredient of our result is a uniform upper bound on the determinant of the Cauchy matrix.
IEEE Transactions on Information Theory 12/2005; · 2.62 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We derive an information-theoretic upper bound on the rate per communication pair in a large ad hoc wireless network. We show that under minimal conditions on the attenuation due to the environment and for networks with a constant density of users, this rate tends to zero as the number of users gets large.
IEEE Transactions on Information Theory 04/2005; · 2.62 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We derive an information theoretic upper bound on the maximum achievable rate per communication pair in a large extended ad-hoc wireless network. We show that under a reasonably weak assumption on the attenuation due to environment, this rate tends to zero as the number of users gets large
Information Theory, 2004. ISIT 2004. Proceedings. International Symposium on; 02/2004