Recognizing sparse perfect elimination bipartite graphs

When applying Gaussian elimination to a sparse matrix, it is desirable to avoid turning zeros into non-zeros to preserve the sparsity. The class of perfect elimination bipartite graphs is closely related to square matrices that Gaussian elimination can be applied to without turning any zero into a non-zero. Existing literature on the recognition of this class and finding suitable pivots mainly focusses on time complexity. For $n \times n$ matrices with m non-zero elements, the currently best known algorithm has a time complexity of $O(n^3/\log n)$. However, when viewed from a practical perspective, the space complexity also deserves attention: it may not be worthwhile to look for a suitable set of pivots for a sparse matrix if this requires $\Omega(n^2)$ space. We present two new algorithms for the recognition of sparse instances: one with a $O(n m)$ time complexity in $\Theta(n^2)$ space and one with a $O(m^2)$ time complexity in $\Theta(m)$ space. Furthermore, if we allow only pivots on the diagonal, our second algorithm can easily be adapted to run in time $O(n m)$

Dimensional Reduction for Conformal Blocks

We consider the dimensional reduction of a CFT, breaking multiplets of the d-dimensional conformal group SO(d+1,1) up into multiplets of SO(d,1). This leads to an expansion of d-dimensional conformal blocks in terms of blocks in d-1 dimensions. In particular, we obtain a formula for 3d conformal blocks as an infinite sum over 2F1 hypergeometric functions with closed-form coefficients.Comment: 12 pages, 1 figur

GMM estimation with noncausal instruments under rational expectations

There is hope for the generalized method of moments (GMM). Lanne and Saikkonen (2011) show that the GMM estimator is inconsistent, when the instruments are lags of noncausal variables. This paper argues that this inconsistency depends on distributional assumptions, that do not always hold. In particular under rational expectations, the GMM estimator is found to be consistent. This result is derived in a linear context and illustrated by simulation of a nonlinear asset pricing model.generalized method of moments, noncausal autoregression, rational expectations

Noncausality and Asset Pricing

Misspecification of agents' information sets or expectation formation mechanisms maylead to noncausal autoregressive representations of asset prices. Annual US stock prices are found to be noncausal, implying that agents' expectations are not revealed to an outside observer such as an econometrician observing only realized market data. A simulation study shows that noncausal processes can be generated by asset-pricing models featuring heterogeneous expectations.noncausal autoregressions, stock prices, heterogeneous expectations

A single-item continuous double auction game

A double auction game with an infinite number of buyers and sellers is introduced. All sellers posses one unit of a good, all buyers desire to buy one unit. Each seller and each buyer has a private valuation of the good. The distribution of the valuations define supply and demand functions. One unit of the good is auctioned. At successive, discrete time instances, a player is randomly selected to make a bid (buyer) or an ask (seller). When the maximum of the bids becomes larger than the minimum of the asks, a transaction occurs and the auction is closed. The players have to choose the value of their bid or ask before the auction starts and use this value when they are selected. Assuming that the supply and demand functions are known, expected profits as functions of the strategies are derived, as well as expected transaction prices. It is shown that for linear supply and demand functions, there exists at most one Bayesian Nash equilibrium. Competitive behaviour is not an equilibrium of the game. For linear supply and demand functions, the sum of the expected profit of the sellers and the buyers is the same for the Bayesian Nash equilibrium and the market where players behave competitively. Connections are made with the ZI-C traders model and the $k$-double auction.Comment: 37 pages, 15 figure

Radial Coordinates for Conformal Blocks

We develop the theory of conformal blocks in CFT_d expressing them as power series with Gegenbauer polynomial coefficients. Such series have a clear physical meaning when the conformal block is analyzed in radial quantization: individual terms describe contributions of descendants of a given spin. Convergence of these series can be optimized by a judicious choice of the radial quantization origin. We argue that the best choice is to insert the operators symmetrically. We analyze in detail the resulting "rho-series" and show that it converges much more rapidly than for the commonly used variable z. We discuss how these conformal block representations can be used in the conformal bootstrap. In particular, we use them to derive analytically some bootstrap bounds whose existence was previously found numerically.Comment: 27 pages, 9 figures; v2: misprints correcte