On the Power of Gradually Increasing Independence

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An iterative PRG method breaks a hard global test into stages that reduce dimension (n → √n → …) and increases independence at each stage so that a k-wise independence seed of size O(k log n) drives the error exponentially small; applying this to load balancing, combinatorial rectangles and halfspaces yields near-optimal constructions (seed roughly log n or log n · log log m with inverse-polynomial error). The core lemma shows products of bounded variables with small total variance have expectations fooled by limited independence, enabling practical PRGs for min-wise hashing, combinatorial tests and small-space derandomization.

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1. 0:00Start
2. 0:19THE OTHER HOLY GRAIL OF PSEUDORANDOMNESS
3. 1:37UNCONDITIONAL CONSTRUCTIONS?
4. 5:37THE GRADUALLY INCREASING INDEPENDENCE PARADIGM
5. 8:27THROWING BALLS INTO BINS
6. 26:20BOUNDED INDEPENDENCE FOR PRODUCTS OF BOUNDED VARIABLES?
7. 31:40THE TEMPLATE
8. 37:48HIGH VARIANCE LOWERS EXPECTATIONS
9. 39:35FOOLING LOW VARIANCE SHAPES
10. 43:36SUMMARY...