We consider risk-neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee’s celebrated moment formula. The theory of regular variation provides the ideal mathematical framework to formulate and prove such results. The practical value of our formulae comes from the vast literature on tail asymptotics and o...

This is a review of the Riemann-Hilbert approach to the large N asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to the large N asymptotics of orthogonal polynomials and its applications to the problem of universality in random matrix models, the double scaling limits, the lar...

This is a review of the Riemann-Hilbert approach to the large N asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to the large N asymptotics of orthogonal polynomials and its applications to the problem of universality in random matrix models, the double scaling limits, the lar...

We present a new method that allows us to get a direct proof of the classical Bernstein asymptotics for the error of the best uniform polynomial approximation of |x| on two symmetric intervals. Note, that in addition, we get asymptotics for the polynomials themselves under a certain renormalization. Also, we solve a problem on asymptotics of the best approximation of sgn (x) on [−1,−a] ∪ [a, 1]...

We study the ultraviolet asymptotics in aane Toda theories. These models are considered as perturbed non-aane Toda theories. We calculate the reeection amplitudes, which relate diierent exponential elds with the same quantum numbers. Using these amplitudes we derive the quantization condition for the vacuum wave function, describing zero-mode dynamics, and calculate the UV asymptotics of the ee...

In this paper, the asymptotic behaviour of the distribution tail of the stationary waiting time W in the GI/GI/2 FCFS queue is studied. Under subexponential-type assumptions on the service time distribution, bounds and sharp asymptotics are given for the probability P{W > x}. We also get asymptotics for the distribution tail of a stationary two-dimensional workload vector and of a stationary qu...

In this paper, the asymptotic behaviour of the distribution tail of the stationary waiting time W in the GI/GI/2 FCFS queue is studied. Under subexponential-type assumptions on the service time distribution, bounds and sharp asymptotics are given for the probability P{W > x}. We also get asymptotics for the distribution tail of a stationary two-dimensional workload vector and of a stationary qu...

We study the ultraviolet asymptotics in affine Toda theories. These models are considered as perturbed non-affine Toda theories. We calculate the reflection amplitudes, which relate different exponential fields with the same quantum numbers. Using these amplitudes we derive the quantization condition for the vacuum wave function, describing zero-mode dynamics, and calculate the UV asymptotics o...

We consider the asymptotics of the distribution of the capture zones associated with the islands nucleated during submonolayer deposition onto a one-dimensional substrate. We use a convolution of the distribution of inter-island gaps, the asymptotics of which is known for a class of nucleation models, to derive the asymptotics for the capture zones. The results are in broad agreement with publi...