Do the Effects of Corruption upon Growth Differ across Political Regimes?

Many studies find that corruption lowers economic growth. However, most of these studies do not consider whether the effects of corruption upon growth differ across countries. This paper investigates whether the association between corruption and economic growth differs between democracies and authoritarian regimes. Consider illegal corruption and legal lobbying, both forms of rent seeking, as imperfect substitutes. Suppose lobbying is easier to do in democracies. Then, lowering corruption in authoritarian regimes could have greater growth benefits because of the lower substitutability between corruption and lobbying in these countries. Using cross-country, annual data from 1984 to 2007, we regress economic growth on: the inverse of the level of corruption, the degree of democracy, and an interaction term combining the two. We find that coefficients are positive on the first two variables. However, the coefficient on the interactive term is negative, suggesting that the benefits upon growth of controlling corruption are actually greater in authoritarian regimes

A matrix Bougerol identity and the Hua-Pickrell measures

We prove a Hermitian matrix version of Bougerol's identity. Moreover, we construct the Hua-Pickrell measures on Hermitian matrices, as stochastic integrals with respect to a drifting Hermitian Brownian motion and with an integrand involving a conjugation by an independent, matrix analogue of the exponential of a complex Brownian motion with drift.Comment: A couple of extra remarks and reference

Ergodic decomposition for inverse Wishart measures on infinite positive-definite matrices

The ergodic unitarily invariant measures on the space of infinite Hermitian matrices have been classified by Pickrell and Olshanski-Vershik. The much-studied complex inverse Wishart measures form a projective family, thus giving rise to a unitarily invariant measure on infinite positive-definite matrices. In this paper we completely solve the corresponding problem of ergodic decomposition for this measure

Determinantal structures in space-inhomogeneous dynamics on interlacing arrays

We introduce a space inhomogeneous generalization of the dynamics on interlacing arrays considered by Borodin and Ferrari. We show that for a certain class of initial conditions the point process associated to the dynamics has determinantal correlation functions and we calculate explicitly, in the form of a double contour integral, the correlation kernel for one of the most classical initial conditions, the densely packed. En route to proving this we obtain some results of independent interest on non-intersecting general pure-birth chains, that generalize the Charlier process, the discrete analogue of Dyson's Brownian motion. Finally, these dynamics provide a coupling between the inhomogeneous versions of the TAZRP and PushTASEP particle systems which appear as projections on the left and right edges of the array respectively.Comment: Minor improvements throughout. Published at Annales Henri Poincar

Infinite p-adic random matrices and ergodic decomposition of p-adic Hua measures

Neretin constructed an analogue of the Hua measures on the infinite $p$-adic matrices $Mat\left(\mathbb{N},\mathbb{Q}_p\right)$. Bufetov and Qiu classified the ergodic measures on $Mat\left(\mathbb{N},\mathbb{Q}_p\right)$ that are invariant under the natural action of $GL(\infty,\mathbb{Z}_p)\times GL(\infty,\mathbb{Z}_p)$. In this paper we solve the problem of ergodic decomposition for the $p$-adic Hua measures introduced by Neretin. We prove that the probability measure governing the ergodic decomposition has an explicit expression which identifies it with a Hall-Littlewood measure on partitions. Our arguments involve certain Markov chains.Comment: Minor revision according to referee reports. To appear Transactions of AM

Random entire functions from random polynomials with real zeros

We point out a simple criterion for convergence of polynomials to a concrete entire function in the Laguerre-P\'{o}lya ($\mathcal{LP}$) class (of all functions arising as uniform limits of polynomials with only real roots). We then use this to show that any random $\mathcal{LP}$ function can be obtained as the uniform limit of rescaled characteristic polynomials of principal submatrices of an infinite unitarily invariant random Hermitian matrix. Conversely, the rescaled characteristic polynomials of principal submatrices of any infinite random unitarily invariant Hermitian matrix converge uniformly to a random $\mathcal{LP}$ function. This result also has a natural extension to $\beta$-ensembles. Distinguished cases include random entire functions associated to the $\beta$-Sine, and more generally $\beta$-Hua-Pickrell, $\beta$-Bessel and $\beta$-Airy point processes studied in the literature.Comment: Improvements following referee report. To appear Advances in Mat

Exact solution of interacting particle systems related to random matrices

We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model of Brownian motions with one-sided collisions, also known as Brownian TASEP, which is equivalent to Brownian last passage percolation. We obtain a formula for the finite dimensional distributions of these particle systems, starting from arbitrary initial condition, in terms of a Fredholm determinant of an explicit kernel. As far as we can tell, in the space-inhomogeneous setting and for general initial condition this is the first time such a result has been proven. We moreover consider the model of non-colliding diffusions, again with polynomial drift and diffusion coefficients, which includes the ones associated to all the classical ensembles of random matrices. We prove that starting from arbitrary initial condition the induced point process has determinantal correlation functions in space and time with an explicit correlation kernel. A key ingredient in our general method of exact solution for both models is the application of the backward in time diffusion flow on certain families of polynomials constructed from the initial condition.Comment: Revised following referee reports. To appear CM

On a gateway between the Laguerre process and dynamics on partitions

Probability measures and stochastic dynamics on matrices and on partitions are related by standard, albeit technical, discrete to continuous scaling limits. In this paper we provide exact relations, that go in both directions, between the eigenvalues of the Laguerre process and certain distinguished dynamics on partitions. This is done by generalizing to the multidimensional setting recent results of Miclo and Patie on linear one-dimensional diffusions and birth and death chains. As a corollary, we obtain an exact relation between the Laguerre and Meixner ensembles. Finally, we explain the deep connections with the Young bouquet and the z-measures on partitions.Comment: Minor improvements throughout. Published at ALE