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3

Modern Mathematical Achievements Accessible to Undergraduates

1

Fundamental inequality of entropy in random walks

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Obtaining conditional probabilities as pushforwards of [0,1]

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Absolute continuity of probabilities on Polish spaces and open sets.

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$\Delta f \le - \lambda f$ then ${\lambda _1}\left( M \right) \ge \lambda$?

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Methods for solving two variable recurrence

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The relations between conservative part and conservativity

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Local concentration of measure on Erdos-Rényi graph

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Finite vertex-transitive graphs that look like infinite vertex-transitive graphs

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Ergodicity for a Probabilistic Cellular Automaton on a finite space

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Weak convergence in measure for negligible sets.

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Compactness of sigma-algebra for the $L^1$ metrics

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Convergence of probability measure and the *-weak convergence ?

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Equivalence of two definitions of Lyapunov exponents

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The property of a Markov measure

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Is the first eigenvalue of a parabolic ends of a Riemanian manifold 0?

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Integral of a harmonic function on a manifold with two non-parabolic ends

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Spanning subgaph with trivial Poisson boundaries

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Is a typical path of a Brownian motion on a torus equidistributed?

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Is there a good concept of a measurable fibration?

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Metrization of weak convergence of signed measures

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Commutators in free groups

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Hutchinson’s formula for asymptotically homogeneous Cantor sets

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Question about entropy

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Relation between entropy of one-parameter group and single elements of this group

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Hidden Markov: representing joint probability for set of observations as a product of two subset probabilities.

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Is there a relationship between Entropy of a fininte distrete probability distribution and the squre sum of the values of probability mass function of that distribution?

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Estimate entropy of a binary process in terms of decay of correlations

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how many nonparabolic ends guarantee a nonconstant harmonic function on Riemannian manifold?

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Gaussian Valued Random Variables in Geometry of Banach Spaces