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Publications Influence

Van Lambalgen's Theorem for uniformly relative Schnorr and computable randomness

- Kenshi Miyabe, Jason Rute
- Mathematics
- 25 September 2012

We correct Miyabe's proof of van Lambalgen's Theorem for truth-table Schnorr randomness (which we will call uniformly relative Schnorr randomness). An immediate corollary is one direction of van… Expand

17 2- PDF

Topics in algorithmic randomness and computable analysis

- Jason Rute
- Mathematics
- 2013

This dissertation develops connections between algorithmic randomness and computable analysis. In the first part, it is shown that computable randomness can be defined robustly on all computable… Expand

10 2

Oscillation and the mean ergodic theorem for uniformly convex Banach spaces

- J. Avigad, Jason Rute
- Mathematics
- Ergodic Theory and Dynamical Systems
- 19 March 2012

Abstract Let $ \mathbb{B} $ be a $p$-uniformly convex Banach space, with $p\geq 2$. Let $T$ be a linear operator on $ \mathbb{B} $, and let ${A}_{n} x$ denote the ergodic average $(1/ n){\mathop{\sum… Expand

21 2- PDF

Computable randomness and betting for computable probability spaces

- Jason Rute
- Mathematics, Computer Science
- Math. Log. Q.
- 25 March 2012

TLDR

14 1- PDF

Oscillation and the mean ergodic theorem

- J. Avigad, Jason Rute
- Mathematics
- 19 March 2012

Let B be a uniformly convex Banach space, let T be a nonexpansive linear operator, and let A_n x denote the ergodic average (1/n) sum_{i 0, the sequence has only finitely many fluctuations greater… Expand

3 1

ALGORITHMIC RANDOMNESS, MARTINGALES AND DIFFERENTIABILITY

- Jason Rute
- 2013

In this paper, a number of almost-everywhere convergence theorems are looked at using computable analysis and algorithmic randomness. These include various martingale convergence theorems and… Expand

7- PDF

Energy randomness

- J. Miller, Jason Rute
- Mathematics, Computer Science
- ArXiv
- 1 September 2015

TLDR

3- PDF

When does randomness come from randomness?

- Jason Rute
- Computer Science, Mathematics
- Theor. Comput. Sci.
- 20 August 2015

TLDR

7- PDF

Schnorr randomness for noncomputable measures

- Jason Rute
- Mathematics, Computer Science
- Inf. Comput.
- 15 July 2016

TLDR

2- PDF

METASTABLE CONVERGENCE THEOREMS

- J. Avigad, Edward T. Dean, Jason Rute
- Mathematics
- 22 August 2011

The dominated convergence theorem implies that if (fn) is a se- quence of functions on a probability space taking values in the interval (0,1), and (fn) converges pointwise a.e., then ( R fn)… Expand

1- PDF

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