We prove theorems about a family of random self-similar sets with overlapping construction on the line. We apply these theorems to estimate the Hausdorff dimension, the Lebesgue measure and prove the existence of interior points of some projections of random self-similar carpets such as the random right-angled Sierpiński gasket, the random Sierpiński carpet and the random Menger sponge.
Meeting ID: 852 4277 3200 Passcode: 103121