Polynomiality of monotone Hurwitz numbers in higher genera

Hurwitz numbers count branched covers of the Riemann sphere with specified ramification, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of these branched covers, related to the expansion of complete symmetric functions in the Jucys-Murphy elements, and have arisen in recent work on the the asymptotic expansion of the Harish-Chandra-Itzykson-Zuber integral. In previous work we gave an explicit formula for monotone Hurwitz numbers in genus zero. In this paper we consider monotone Hurwitz numbers in higher genera, and prove a number of results that are reminiscent of those for classical Hurwitz numbers. These include an explicit formula for monotone Hurwitz numbers in genus one, and an explicit form for the generating function in arbitrary positive genus. From the form of the generating function we are able to prove that monotone Hurwitz numbers exhibit a polynomiality that is reminiscent of that for the classical Hurwitz numbers, i.e., up to a specified combinatorial factor, the monotone Hurwitz number in genus g with ramification specified by a given partition is a polynomial indexed by g in the parts of the partition.Comment: 23 page

Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers

This article introduces mixed double Hurwitz numbers, which interpolate combinatorially between the classical double Hurwitz numbers studied by Okounkov and the monotone double Hurwitz numbers introduced recently by Goulden, Guay-Paquet and Novak. Generalizing a result of Okounkov, we prove that a certain generating series for the mixed double Hurwitz numbers solves the 2-Toda hierarchy of partial differential equations. We also prove that the mixed double Hurwitz numbers are piecewise polynomial, thereby generalizing a result of Goulden, Jackson and Vakil

Monotone Hurwitz numbers and the HCIZ integral

In this article, we prove that the complex convergence of the HCIZ free energy is equivalent to the non-vanishing of the HCIZ integral in a neighbourhood of $z=0$. Our approach is based on a combinatorial model for the Maclaurin coefficients of the HCIZ integral together with classical complex-analytic techniques.Comment: 13 page

Microelectrode study of pore size, ion size, and solvent effects on the charge/discharge behavior of microporous carbons for electrical double-layer capacitors

The capacitive behavior of TiC-derived carbon powders in two different electrolytes, NEt4BF4 in acetonitrile AN and NEt4BF4 in propylene carbonate PC, was studied using the cavity microelectrode CME technique. Comparisons of the cyclic voltammograms recorded at 10–1000 mV/s enabled correlation between adsorbed ion sizes and pore sizes, which is important for understanding the electrochemical capacitive behavior of carbon electrodes for electrical double-layer capacitor applications. The CME technique also allows a fast selection of carbon electrodes with matching pore sizes different sizes are needed for the negative and positive electrodes for the respective electrolyte system. Comparison of electrochemical capacitive behavior of the same salt, NEt4BF4, in different solvents, PC and AN, has shown that different pore sizes are required for different solvents, because only partial desolvation of ions occurs during the double-layer charging. Squeezing partially solvated ions into subnanometer pores, which are close to the desolvated ion size, may lead to distortion of the shape of cyclic voltammograms

Monotone Hurwitz numbers in genus zero

Hurwitz numbers count branched covers of the Riemann sphere with specified ramification data, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of the branched covers counted by the Hurwitz numbers, and have arisen in recent work on the the asymptotic expansion of the Harish-Chandra-Itzykson-Zuber integral. In this paper we begin a detailed study of monotone Hurwitz numbers. We prove two results that are reminiscent of those for classical Hurwitz numbers. The first is the monotone join-cut equation, a partial differential equation with initial conditions that characterizes the generating function for monotone Hurwitz numbers in arbitrary genus. The second is our main result, in which we give an explicit formula for monotone Hurwitz numbers in genus zero.Comment: 22 pages, submitted to the Canadian Journal of Mathematic

How Much Do Firms Hedge With Derivatives?

For 234 large non-financial corporations using derivatives, we report the magnitude of their risk exposure hedged by financial derivatives. If interest rates, currency exchange rates, and commodity prices change simultaneously by three standard deviations, the median firm\u27s derivatives portfolio, at most, generates $15 million in cash and$31 million in value. These amounts are modest relative to firm size, and operating and investing cash flows, and other benchmarks. Corporate derivatives use appears to be a small piece of non-financial firms’ overall risk profile. This suggests a need to rethink past empirical research documenting the importance of firms’ derivative use

Field theoretic description of the abelian and non-abelian Josephson effect

We formulate the Josephson effect in a field theoretic language which affords a straightforward generalization to the non-abelian case. Our formalism interprets Josephson tunneling as the excitation of pseudo-Goldstone bosons. We demonstrate the formalism through the consideration of a single junction separating two regions with a purely non-abelian order parameter and a sandwich of three regions where the central region is in a distinct phase. Applications to various non-abelian symmetry breaking systems in particle and condensed matter physics are given.Comment: 10 pages no figure

Properties of Implied Cost of Capital Using Analysts’ Forecasts

We evaluate the influence of measurement error in analysts’ forecasts on the accuracy of implied cost of capital estimates from various implementations of the ‘implied cost of capital’ approach, and develop corrections for the measurement error. The implied cost of capital approach relies on analysts’ short- and long-term earnings forecasts as proxies for the market’s expectation of future earnings, and solves for the implied discount rate that equates the present value of the expected future payoffs to the current stock price. We document predictable error in the implied cost of capital estimates resulting from analysts’ forecasts that are sluggish with respect to information in past stock returns. We propose two methods to mitigate the influence of sluggish forecasts on the implied cost of capital estimates. These methods substantially improve the ability of the implied cost of capital estimates to explain cross-sectional variation in future stock returns, which is consistent with the corrections being effective in mitigating the error in the estimates due to analysts’ sluggishness