elasticsearch filtering by the size of a field that is an array

I would have a look at the script filter. The following filter should return only the documents that have at least 10 elements in the fieldname field, which is an array. Keep in mind that this could be expensive depending on how many documents you have in your index.

"filter" : {
    "script" : {
        "script" : "doc['fieldname'].values.length > 10"
    }
}

Regarding the second question: do you really have an empty array there? Or is it just an array field with no value? You can use the missing filter to get documents which have no value for a specific field:

"filter" : {
    "missing" : { "field" : "user" }
}

Otherwise I guess you need to use scripting again, similarly to what I suggested above, just with a different length as input. If the length is constant I'd put it in the params section so that the script will be cached by elasticsearch and reused, since it's always the same:

"filter" : {
    "script" : {
        "script" : "doc['fieldname'].values.length > params.param1"
        "params" : {
            "param1" : 10
        }
    }
}

javanna's answer is correct on Elasticsearch 1.3.x and earlier, since 1.4 the default scripting module has changed to groovy (was mvel).

To answer OP's question.

On Elasticsearch 1.3.x and earlier, use this code:

"filter" : {
    "script" : {
        "script" : "doc['fieldname'].values.length > 10"
    }
}

On Elasticsearch 1.4.x and later, use this code:

"filter" : {
    "script" : {
        "script" : "doc['fieldname'].values.size() > 10"
    }
}

Additionally, on Elasticsearch 1.4.3 and later, you will need to enable the dynamic scripting as it has been disabled by default, because of security issue. See: https://www.elastic.co/guide/en/elasticsearch/reference/1.4/modules-scripting.html