Display Random Post in Author Page

use this query in themes functions.php

function ng_author_query( $query ) {
    if ( $query->is_author()
        && $query->is_main_query() ) {
            // your code to set $current_user_name here
            $query->set( 'orderby', 'rand' );
    }
}
add_action( 'pre_get_posts', 'ng_author_query' );

Let me know if you have any problem?

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