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3 results

  • Strong Shannon–McMillan–Breiman’s theorem for locally compact groups

  • Part of
  • Behrang Forghani, May Nguyen
  • Journal:
    Canadian Mathematical Bulletin / Volume 66 / Issue 4 / December 2023
    Published online by Cambridge University Press:
    05 May 2023, pp. 1274-1279
    Print publication:
    December 2023
    • Article
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      • Open access
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  • We prove that for a vast class of random walks on a compactly generated group, the exponential growth of convolutions of a probability density function along almost every sample path is bounded by the growth of the group. As an application, we show that the almost sure and $L^1$ convergences of the Shannon–McMillan–Breiman theorem hold for compactly supported random walks on compactly generated groups with subexponential growth.

  • Chapter 15 - The Transition of Reputation: Gerald Griffin

  • from Part III - Reputations
  • Edited by Claire Connolly, University College Cork
  • Book:
    Irish Literature in Transition, 1780–1830
    Published online:
    28 February 2020
    Print publication:
    12 March 2020, pp 292-305

  • Summary

    This chapter moves the reputation of Gerald Griffin’s The Collegians outside a predominantly Catholic context and argues that the transnational dimensions of the novel connect local with global forces. Griffin’s depiction of multicultural Catholic characters suggests a shifting version of Irish identity that can be constructed outside of morality and religion. The chapter highlights the cultural and political moments that shaped Griffin’s standing and suggests new ways of framing his achievements. It also shows Griffin was phased out of an emerging nationalist narrative of Irish literature, in part via the political reception of William Carleton in nationalist and Fenian newspapers of the 1840s. Meanwhile the movements in academic criticism in the 1960s that rescued Dion Boucicault from obscurity had the effect of reducing Griffin’s reputation to the creator of the Colleen Bawn.

  • 4 - On Time, Frequency, and Gauss

  • from Part I - Basics and Constraints
  • Patrick Flandrin
  • Book:
    Explorations in Time-Frequency Analysis
    Published online:
    22 August 2018
    Print publication:
    06 September 2018, pp 29-34

  • Summary

    Gaussian functions are central throughout the book. They are introduced as basic elementary waveforms whose versatility can be used for establishing a continuum of representations between the "natural" (Shannon-Nyquist-like) representation in time to the dual (Fourier) representation in frequency. This allows for a first introduction of a joint (Gabor) time-frequency representation.