We prove that the free energy of log-gamma polymer between lattice points (1, 1) and (M, N) converges to GUE Tracy–Widom distribution in $$M^{1/3}$$ scaling, provided N/M remains bounded away from zero infinity. this result for model with inverse gamma weights any shape parameter $$\theta >0$$ furthermore establish a moderate deviation estimate upper tail case. Finally, we consider non i.i.d. s...

We draw on portfolio theory and international diversification in order to analyse strategies allowing to reduce emerging economies’ exposure to exchange-rate risk. We show in particular that it may be efficient for an investor, in terms of maximising the return-to-risk ratio, to build up a portfolio of emerging-country assets denominated in local currency unhedged against currency risk compared...

We study a model of random graphs where each edge is drawn independently (but not necessarily identically distributed) from the others, and then assigned weight. When mean degree such graph low, it known that spectrum adjacency matrix $A$ deviates significantly its expected value $\mathbb{E} A$ . In contrast, we show over wide range parameters top eigenvalues non-backtracking $B$ – whose powers...