Zobrazeno 1 - 10
of 214
pro vyhledávání: '"Ipsen, J."'
Publikováno v:
Phys. Rev. E 103, 022201 (2021)
We consider a generic nonlinear extension of May's 1972 model by including all higher-order terms in the expansion around the chosen fixed point (placed at the origin) with random Gaussian coefficients. The ensuing analysis reveals that as long as th
Externí odkaz:
http://arxiv.org/abs/2008.04622
Autor:
Ipsen, J. R., Peterson, A. D. H.
In the study of randomly connected neural network dynamics there is a phase transition from a `simple' state with few equilibria to a `complex' state characterised by the number of equilibria growing exponentially with the neuron population. Such pha
Externí odkaz:
http://arxiv.org/abs/1907.07293
Autor:
Ipsen, J. R.
We define a new matrix-valued stochastic process with independent stationary increments from the Laguerre Unitary Ensemble, which in a certain sense may be considered a matrix generalisation of the gamma process. We show that eigenvalues of this matr
Externí odkaz:
http://arxiv.org/abs/1903.00176
Autor:
Ipsen, J. R., Forrester, P. J.
We present a null model for single- and multi-layered complex systems constructed using homogeneous and isotropic random Gaussian maps. By means of a Kac-Rice formalism, we show that the mean number of fixed points can be calculated as the expectatio
Externí odkaz:
http://arxiv.org/abs/1807.05790
A truncation of a Haar distributed orthogonal random matrix gives rise to a matrix whose eigenvalues are either real or complex conjugate pairs, and are supported within the closed unit disk. This is also true for a product $P_m$ of $m$ independent t
Externí odkaz:
http://arxiv.org/abs/1708.00967
Autor:
Ipsen, J. R.
We consider stability in a class of random non-linear dynamical systems characterised by a relaxation rate together with a Gaussian random vector field which is white-in-time and spatial homogeneous and isotropic. We will show that in the limit of la
Externí odkaz:
http://arxiv.org/abs/1705.05047
We investigate spectral properties of a Hermitised random matrix product which, contrary to previous product ensembles, allows for eigenvalues on the full real line. We prove that the eigenvalues form a bi-orthogonal ensemble, which reduces asymptoti
Externí odkaz:
http://arxiv.org/abs/1702.07100
Autor:
Forrester, P. J., Ipsen, J. R.
We study Muttalib--Borodin ensembles --- particular eigenvalue PDFs on the half-line --- with classical weights, i.e. Laguerre, Jacobi or Jacobi prime. We show how the theory of the Selberg integral, involving also Jack and Schur polynomials, natural
Externí odkaz:
http://arxiv.org/abs/1612.06517
Autor:
Forrester, P. J., Ipsen, J. R.
Random matrices formed from i.i.d. standard real Gaussian entries have the feature that the expected number of real eigenvalues is non-zero. This property persists for products of such matrices, independently chosen, and moreover it is known that as
Externí odkaz:
http://arxiv.org/abs/1608.04097
Isotropic Brownian motions over complex fields as a solvable model for May-Wigner stability analysis
Autor:
Ipsen, J. R., Schomerus, H.
Publikováno v:
J. Phys. A 49 (2016) 385201
We consider matrix-valued stochastic processes known as isotropic Brownian motions, and show that these can be solved exactly over complex fields. While these processes appear in a variety of questions in mathematical physics, our main motivation is
Externí odkaz:
http://arxiv.org/abs/1602.06364