@article{10862, abstract = {We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu's theorem. Our previous works [4], [5] established these results in the bulk spectrum, the current paper completely settles the problem at the spectral edges provided they have the typical square-root behavior. The key element of our proof is to compensate the deterioration of the stability of the subordination equations by sharp error estimates that properly account for the local density near the edge. Our results also hold if the Haar unitary matrix is replaced by the Haar orthogonal matrix.}, author = {Bao, Zhigang and Erdös, László and Schnelli, Kevin}, issn = {0022-1236}, journal = {Journal of Functional Analysis}, keywords = {Analysis}, number = {7}, publisher = {Elsevier}, title = {{Spectral rigidity for addition of random matrices at the regular edge}}, doi = {10.1016/j.jfa.2020.108639}, volume = {279}, year = {2020}, } @article{10867, abstract = {In this paper we find a tight estimate for Gromov’s waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds on the curvature (CAT(ϰ)-spaces), and establish similar result for normed spaces.}, author = {Akopyan, Arseniy and Karasev, Roman}, issn = {1687-0247}, journal = {International Mathematics Research Notices}, keywords = {General Mathematics}, number = {3}, pages = {669--697}, publisher = {Oxford University Press}, title = {{Waist of balls in hyperbolic and spherical spaces}}, doi = {10.1093/imrn/rny037}, volume = {2020}, year = {2020}, } @misc{9799, abstract = {Fitness interactions between mutations can influence a population’s evolution in many different ways. While epistatic effects are difficult to measure precisely, important information is captured by the mean and variance of log fitnesses for individuals carrying different numbers of mutations. We derive predictions for these quantities from a class of simple fitness landscapes, based on models of optimizing selection on quantitative traits. We also explore extensions to the models, including modular pleiotropy, variable effect sizes, mutational bias and maladaptation of the wild type. We illustrate our approach by reanalysing a large dataset of mutant effects in a yeast snoRNA. Though characterized by some large epistatic effects, these data give a good overall fit to the non-epistatic null model, suggesting that epistasis might have limited influence on the evolutionary dynamics in this system. We also show how the amount of epistasis depends on both the underlying fitness landscape and the distribution of mutations, and so is expected to vary in consistent ways between new mutations, standing variation and fixed mutations.}, author = {Fraisse, Christelle and Welch, John J.}, publisher = {Royal Society of London}, title = {{Simulation code for Fig S1 from the distribution of epistasis on simple fitness landscapes}}, doi = {10.6084/m9.figshare.7957469.v1}, year = {2020}, } @misc{9798, abstract = {Fitness interactions between mutations can influence a population’s evolution in many different ways. While epistatic effects are difficult to measure precisely, important information is captured by the mean and variance of log fitnesses for individuals carrying different numbers of mutations. We derive predictions for these quantities from a class of simple fitness landscapes, based on models of optimizing selection on quantitative traits. We also explore extensions to the models, including modular pleiotropy, variable effect sizes, mutational bias and maladaptation of the wild type. We illustrate our approach by reanalysing a large dataset of mutant effects in a yeast snoRNA. Though characterized by some large epistatic effects, these data give a good overall fit to the non-epistatic null model, suggesting that epistasis might have limited influence on the evolutionary dynamics in this system. We also show how the amount of epistasis depends on both the underlying fitness landscape and the distribution of mutations, and so is expected to vary in consistent ways between new mutations, standing variation and fixed mutations.}, author = {Fraisse, Christelle and Welch, John J.}, publisher = {Royal Society of London}, title = {{Simulation code for Fig S2 from the distribution of epistasis on simple fitness landscapes}}, doi = {10.6084/m9.figshare.7957472.v1}, year = {2020}, } @article{6488, abstract = {We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish.}, author = {Cipolloni, Giorgio and Erdös, László}, issn = {20103271}, journal = {Random Matrices: Theory and Application}, number = {3}, publisher = {World Scientific Publishing}, title = {{Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices}}, doi = {10.1142/S2010326320500069}, volume = {9}, year = {2020}, }