## Log-Sobolev inequalities and sampling from log-concave distributions.(English)Zbl 0931.68140

Summary: We consider the problem of sampling according to a distribution with log-concave density $$F$$ over a convex body $$K\subseteq \mathbb{R}^n$$. The sampling is done using a biased random walk and we give improved polynomial upper bounds on the time to get a sample point with distribution close to $$F$$.

### MSC:

 68W05 Nonnumerical algorithms 60G50 Sums of independent random variables; random walks

### Keywords:

log-concave distributions
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### References:

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