The replica method has previously been used to calculate the semicircular averaged eigenvalue spectrum of the Gaussian orthogonal ensemble of real symmetric N x N random matrices in the limit where N + CC. In this paper we develop a perturbative scheme which, within this same replica framework, is used to calculate the corrections within this semicircular band of eigenvalues to order 1/ N and 1/ N2. Comparison is made between these results and previously published work by other authors on the corrections to order 1/ N. A new and straightforward self-consistency argument is presented and used to derive the shape of the averaged eigenvalue spectrum when N is large but finite and the scaling behaviour of this averaged eigenvalue spectrum near the band edges is demonstrated in a straightforward fashion. Some comments are made on the relation of our results to those of field theoretical calculations in zero dimensions.

This paper investigates the effects of social media on entrepreneurial opportunity recognition. Combining the internal and external approaches of opportunity recognition, the study analyzes how social media influences the entrepreneurs in discovering new entrepreneurial opportunities. Structural equation modeling was used in this study, using the variance-based partial least squares (PLS)–structural equation modeling (SEM), on a sample of 354 entrepreneurs. We concluded that social media directly and positively influences entrepreneurial opportunity recognition while entrepreneurial alertness (internal approach) and social networks (external approach) partially mediates its indirect effects on entrepreneurial opportunity recognition. The study contributes to the existing literature by bringing new insights into the entrepreneurial opportunity recognition process by focusing on a poorly represented factor in the literature, social media.

Following a Geometrical Brownian Motion extension into an Irrational Fractional Brownian Motion model, we re-examine agent behaviour reacting to time dependent news on the logreturns thereby modifying a financial market evolution. We specifically discuss the role of financial news or economic information positive or negative feedback of such irrational (or contrarian) agents upon the price evolution. We observe a kink-like effect reminiscent of soliton behaviour, suggesting how analysts' forecasts errors induce stock prices to adjust accordingly, thereby proposing a measure of the irrational force in a market.

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