Help in widget "summarize posts"

[+author_avatar+] is not a viable placeholder. You can’t just use a random placeholder and expect it to be magically populated. Use the [+help+] placeholder to print out available placeholders (or use help=”1″ as part of your shortcode). There are a few bonus placeholders provided, but mostly, they correspond exactly to the columns from wp_posts and the related meta_keys from wp_postmeta.

If you absolutely require the avatar, you would have to do this manually via PHP.