Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices

Spatially and temporally inhomogeneous evolution of one-dimensional vicious walkers with wall restriction is studied. We show that its continuum version is equivalent with a noncolliding system of stochastic processes called Brownian meanders. Here the Brownian meander is a temporally inhomogeneous process introduced by Yor as a transform of the Bessel process that is a motion of radial coordinate of the three-dimensional Brownian motion represented in the spherical coordinates. It is proved that the spatial distribution of vicious walkers with a wall at the origin can be described by the eigenvalue-statistics of Gaussian ensembles of Bogoliubov-deGennes Hamiltonians of the mean-field theory of superconductivity, which have the particle-hole symmetry. We report that the time evolution of the present stochastic process is fully characterized by the change of symmetry classes from the type $C$ to the type $C$I in the nonstandard classes of random matrix theory of Altland and Zirnbauer. The relation between the non-colliding systems of the generalized meanders of Yor, which are associated with the even-dimensional Bessel processes, and the chiral random matrix theory is also clarified.Comment: REVTeX4, 16 pages, 4 figures. v2: some additions and correction

Universal energy distribution for interfaces in a random field environment

We study the energy distribution function $\rho (E)$ for interfaces in a random field environment at zero temperature by summing the leading terms in the perturbation expansion of $\rho (E)$ in powers of the disorder strength, and by taking into account the non perturbational effects of the disorder using the functional renormalization group. We have found that the average and the variance of the energy for one-dimensional interface of length $L$ behave as, $_{R}\propto L\ln L$, $\Delta E_{R}\propto L$, while the distribution function of the energy tends for large $L$ to the Gumbel distribution of the extreme value statistics.Comment: 4 pages, 2 figures, revtex4; the distribution function of the total and the disorder energy is include

Canonical moments and random spectral measures

We study some connections between the random moment problem and the random matrix theory. A uniform draw in a space of moments can be lifted into the spectral probability measure of the pair (A,e) where A is a random matrix from a classical ensemble and e is a fixed unit vector. This random measure is a weighted sampling among the eigenvalues of A. We also study the large deviations properties of this random measure when the dimension of the matrix grows. The rate function for these large deviations involves the reversed Kullback information.Comment: 32 pages. Revised version accepted for publication in Journal of Theoretical Probabilit

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Subcutaneous daratumumab plus standard treatment regimens in patients with multiple myeloma across lines of therapy (PLEIADES): an open-label Phase II study

© 2020 The Authors. Daratumumab is a CD38-targeting monoclonal antibody approved for intravenous (IV) infusion for multiple myeloma (MM). We describe the Phase II PLEIADES study of a subcutaneous formulation of daratumumab (DARA SC) in combination with standard-of-care regimens: DARA SC plus bortezomib/lenalidomide/dexamethasone (D-VRd) for transplant-eligible newly diagnosed MM (NDMM); DARA SC plus bortezomib/melphalan/prednisone (D-VMP) for transplant-ineligible NDMM; and DARA SC plus lenalidomide/dexamethasone (D-Rd) for relapsed/refractory MM. In total, 199 patients were treated (D-VRd, n = 67; D-VMP, n = 67; D-Rd, n = 65). The primary endpoints were met for all cohorts: the ≥very good partial response (VGPR) rate after four 21-day induction cycles for D-VRd was 71·6% [90% confidence interval (CI) 61·2–80·6%], and the overall response rates (ORRs) for D-VMP and D-Rd were 88·1% (90% CI 79·5–93·9%) and 90·8% (90% CI 82·6–95·9%). With longer median follow-up for D-VMP and D-Rd (14·3 and 14·7 months respectively), responses deepened (ORR: 89·6%, 93·8%; ≥VGPR: 77·6%, 78·5%), and minimal residual disease–negativity (10‒5) rates were 16·4% and 15·4%. Infusion-related reactions across all cohorts were infrequent (≤9·0%) and mild. The median DARA SC administration time was 5 min. DARA SC with standard-of-care regimens demonstrated comparable clinical activity to DARA IV–containing regimens, with low infusion-related reaction rates and reduced administration time

Strategic Experimentation with Exponential Bandits

We analyze a game of strategic experimentation with two-armed bandits whose risky arm might yield payoffs after exponentially distributed random times. Free-riding causes an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with beliefs as the state variable. We construct the unique symmetric Markovian equilibrium of the game, followed by various asymmetric ones. There is no equilibrium where all players use simple cut-off strategies. Equilibria where players switch finitely often between experimenting and free-riding all yield a similar pattern of information acquisition, greater efficiency being achieved when the players share the burden of experimentation more equitably. When players switch roles infinitely often, they can acquire an approximately efficient amount of information, but still at an inefficient rate. In terms of aggregate payoffs, all these asymmetric equilibria dominate the symmetric one wherever the latter prescribes simultaneous use of both arms. Copyright The Econometric Society 2005.