3 problems

Positive-measure discontinuity conjecture for the lower spectral radius
Positive-measure discontinuity conjecture. The set of discontinuities of $\check{\varrho}$ has positive Lebesgue measure. This is presented as a weaker version of the resist-impuri…
openFrom paperscontinuity lower-spectral-radius matrix-products
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3
The resist-impurities conjecture for pairs of $2\times2$ matrices
The resist-impurities conjecture. The set of pairs $(H,R)\in\mathcal{H}\times\mathcal{E}$ that resist impurities has full Lebesgue measure in $\mathcal{H}\times\mathcal{E}$ . This c…
openFrom papersergodic-theory lower-spectral-radius matrix-products
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3
Protasov's conjecture on spectrum-maximizing and spectrum-minimizing products
Let $r$ be an odd integer, and let $A_1,A_2$ be the $(r-1)\times(r-1)$ matrices defined by … and $(A_s)_{ij}=0$ otherwise, for $s=1,2$ . A product is an s.m.p. if it is a spectrum-m…
openFrom papersjoint-spectral-radius lower-spectral-radius matrix-products
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3

Positive-measure discontinuity conjecture for the lower spectral radius