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  Congruences with Eisenstein series and mu-invariants 

  Bellaïche, Joël; Pollack, Robert (Foundation Compositio Mathematica, 2019-05)

  We study the variation of -invariants in Hida families with residually reducible Galois representations. We prove a lower bound for these invariants which is often expressible in terms of the -adic zeta function. This lower ...
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  A multiple stochastic integral criterion for almost sure limit theorems 

  Bercu, Bernard; Nourdin, Ivan; Taqqu, Murad S. (2009-04-15)

  In this paper, we study almost sure entral limit theorems for multiple stohasti integrals and provide a riterion based on the kernel of these multiple integrals. We apply our result to normalized partial sums of Hermite ...
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  Geodesic paths for quantum many-body systems 

  Tomka, Michael; Souza, Tiago; Rosenberg, Steven; Polkovnikov, Anatoli (American Physical Society, 2016-06-19)

  We propose a method to obtain optimal protocols for adiabatic ground-state preparation near the adiabatic limit, extending earlier ideas from [D. A. Sivak and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)] to quantum ...
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  Enabling adiabatic passages between disjoint regions in parameter space through topological transitions 

  Souza, Tiago; Tomka, Michael; Kolodrubetz, Michael; Rosenberg, Steven; Polkovnikov, Anatoli (AMER PHYSICAL SOC, 2016-09-09)

  We explore topological transitions in parameter space in order to enable adiabatic passages between regions adiabatically disconnected within a given parameter manifold. To this end, we study the Hamiltonian of two coupled ...
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  Large deviations and averaging for systems of slow–fast reaction–diffusion equations 

  Hu, Wenqing; Salins, Michael; Spiliopoulos, Konstantinos (2017-10-07)

  We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation ...
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  Nonlinear stability of source defects in oscillatory media 

  Beck, Margaret; Nguyen, Toan; Sandstede, Bjorn; Zumbrun, Kevin (2018-02-21)

  In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each ...
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  Localized radial roll patterns in higher space dimensions 

  Bramburger, Jason J.; Altschuler, Dylan J.; Avery, Chloe I.; Sangsawang, Tharathep; Beck, Margaret; Carter, Paul; Sandstede, Bjorn (2018)

  Localized roll patterns are structures that exhibit a spatially periodic profile in their center. When following such patterns in a system parameter in one space dimension, the length of the spatial interval over which ...
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  Equivalences and counterexamples between several definitions of the uniform large deviations principle 

  Salins, Michael (2018-09-18)

  This paper explores the equivalences between four definitions of uniform large deviations principles and uniform Laplace principles found in the literature. Counterexamples are presented to illustrate the differences between ...
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  Rigorous justification of Taylor dispersion via center manifolds and hypocoercivity 

  Beck, Margaret; Wayne, Clarence Eugene; Chaudhary, Osman (2018)

  Taylor diffusion (or dispersion) refers to a phenomenon discovered experimentally by Taylor in the 1950s where a solute dropped into a pipe with a background shear flow experiences diffusion at a rate proportional to 1/ν, ...
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  Uniform large deviation principles for Banach space valued stochastic differential equations 

  Budhiraja, Amarjit; Dupuis, Paul; Salins, Michael (2018-03-05)

  We prove a large deviation principle (LDP) for a general class of Banach space valued stochastic differential equations (SDE) that is uniform with respect to initial conditions in bounded subsets of the Banach space. A key ...

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